結果
| 問題 | No.3228 Very Large Fibonacci Sum |
| ユーザー |
 syun0713
|
| 提出日時 | 2026-11-07 18:42:43 |
| 言語 | C++23(gnu拡張gcc16) (gcc 16.2.0 + boost 1.92.0 + ACL) |
| 結果 |
AC
不安定
|
| 実行時間 | 1 ms / 2,000 ms |
| + 643µs | |
| コード長 | 76,142 bytes |
| 記録 | |
| コンパイル時間 | 7,646 ms |
| コンパイル使用メモリ | 433,468 KB |
| 実行使用メモリ | 9,900 KB |
| 最終ジャッジ日時 | 2026-11-07 18:42:52 |
| 合計ジャッジ時間 | 8,845 ms |
|
ジャッジサーバーID （参考情報） |
judge2_0 / judge4_0 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 23 |
ソースコード
//ACL
#ifndef ATCODER_INTERNAL_BITOP_HPP
#define ATCODER_INTERNAL_BITOP_HPP 1
#ifdef _MSC_VER
#include <intrin.h>
#include<cassert>
#endif
namespace atcoder {
namespace internal {
int ceil_pow2(int n) {
int x = 0;
while ((1U << x) < (unsigned int)(n)) x++;
return x;
}
int bsf(unsigned int n) {
#ifdef _MSC_VER
unsigned long index;
_BitScanForward(&index, n);
return index;
#else
return __builtin_ctz(n);
#endif
}
}
}
#endif
#ifndef ATCODER_INTERNAL_MATH_HPP
#define ATCODER_INTERNAL_MATH_HPP 1
#include <utility>
namespace atcoder {
namespace internal {
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
struct barrett {
unsigned int _m;
unsigned long long im;
barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
unsigned int umod() const { return _m; }
unsigned int mul(unsigned int a, unsigned int b) const {
unsigned long long z = a;
z *= b;
#ifdef _MSC_VER
unsigned long long x;
_umul128(z, im, &x);
#else
unsigned long long x =
(unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
unsigned int v = (unsigned int)(z - x * _m);
if (_m <= v) v += _m;
return v;
}
};
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
if (m == 1) return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = safe_mod(x, m);
while (n) {
if (n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
constexpr bool is_prime_constexpr(int n) {
if (n <= 1) return false;
if (n == 2 || n == 7 || n == 61) return true;
if (n % 2 == 0) return false;
long long d = n - 1;
while (d % 2 == 0) d /= 2;
int v[] = { 2,7,61 };
for (long long a : v) {
long long t = d;
long long y = pow_mod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1) {
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0) {
return false;
}
}
return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
a = safe_mod(a, b);
if (a == 0) return { b, 0 };
long long s = b, t = a;
long long m0 = 0, m1 = 1;
while (t) {
long long u = s / t;
s -= t * u;
m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
if (m0 < 0) m0 += b / s;
return { s, m0 };
}
constexpr int primitive_root_constexpr(int m) {
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0) x /= 2;
for (int i = 3; (long long)(i)*i <= x; i += 2) {
if (x % i == 0) {
divs[cnt++] = i;
while (x % i == 0) {
x /= i;
}
}
}
if (x > 1) {
divs[cnt++] = x;
}
for (int g = 2;; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);
}
}
#endif
#ifndef ATCODER_INTERNAL_QUEUE_HPP
#define ATCODER_INTERNAL_QUEUE_HPP 1
#include <vector>
namespace atcoder {
namespace internal {
template <class T> struct simple_queue {
std::vector<T> payload;
int pos = 0;
void reserve(int n) { payload.reserve(n); }
int size() const { return int(payload.size()) - pos; }
bool empty() const { return pos == int(payload.size()); }
void push(const T& t) { payload.push_back(t); }
T& front() { return payload[pos]; }
void clear() {
payload.clear();
pos = 0;
}
void pop() { pos++; }
};
}
}
#endif
#ifndef ATCODER_INTERNAL_SCC_HPP
#define ATCODER_INTERNAL_SCC_HPP 1
#include <algorithm>
#include <utility>
#include <vector>
namespace atcoder {
namespace internal {
template <class E> struct csr {
std::vector<int> start;
std::vector<E> elist;
csr(int n, const std::vector<std::pair<int, E>>& edges)
: start(n + 1), elist(edges.size()) {
for (auto e : edges) {
start[e.first + 1]++;
}
for (int i = 1; i <= n; i++) {
start[i] += start[i - 1];
}
auto counter = start;
for (auto e : edges) {
elist[counter[e.first]++] = e.second;
}
}
};
struct scc_graph {
public:
scc_graph(int n) : _n(n) {}
int num_vertices() { return _n; }
void add_edge(int from, int to) { edges.push_back({ from, {to} }); }
std::pair<int, std::vector<int>> scc_ids() {
auto g = csr<edge>(_n, edges);
int now_ord = 0, group_num = 0;
std::vector<int> visited, low(_n), ord(_n, -1), ids(_n);
visited.reserve(_n);
auto dfs = [&](auto self, int v) -> void {
low[v] = ord[v] = now_ord++;
visited.push_back(v);
for (int i = g.start[v]; i < g.start[v + 1]; i++) {
auto to = g.elist[i].to;
if (ord[to] == -1) {
self(self, to);
low[v] = std::min(low[v], low[to]);
}
else {
low[v] = std::min(low[v], ord[to]);
}
}
if (low[v] == ord[v]) {
while (true) {
int u = visited.back();
visited.pop_back();
ord[u] = _n;
ids[u] = group_num;
if (u == v) break;
}
group_num++;
}
};
for (int i = 0; i < _n; i++) {
if (ord[i] == -1) dfs(dfs, i);
}
for (auto& x : ids) {
x = group_num - 1 - x;
}
return { group_num, ids };
}
std::vector<std::vector<int>> scc() {
auto ids = scc_ids();
int group_num = ids.first;
std::vector<int> counts(group_num);
for (auto x : ids.second) counts[x]++;
std::vector<std::vector<int>> groups(ids.first);
for (int i = 0; i < group_num; i++) {
groups[i].reserve(counts[i]);
}
for (int i = 0; i < _n; i++) {
groups[ids.second[i]].push_back(i);
}
return groups;
}
private:
int _n;
struct edge {
int to;
};
std::vector<std::pair<int, edge>> edges;
};
}
}
#endif
#ifndef ATCODER_INTERNAL_TYPE_TRAITS_HPP
#define ATCODER_INTERNAL_TYPE_TRAITS_HPP 1
#include <cassert>
#include <numeric>
#include <type_traits>
namespace atcoder {
namespace internal {
#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int128 =
typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value,
__uint128_t,
unsigned __int128>;
template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
is_signed_int128<T>::value ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value&&
std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value&&
std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value,
make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type>::type;
#else
template <class T> using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
typename std::conditional<is_integral<T>::value&& std::is_signed<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<is_integral<T>::value&&
std::is_unsigned<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type;
#endif
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T> using to_unsigned_t = typename to_unsigned<T>::type;
}
}
#endif
#ifndef ATCODER_MODINT_HPP
#define ATCODER_MODINT_HPP 1
#include <cassert>
#include <numeric>
#include <type_traits>
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
struct modint_base {};
struct static_modint_base : modint_base {};
template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;
}
template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
using mint = static_modint;
public:
static constexpr int mod() { return m; }
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
static_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
static_modint(T v) {
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
static_modint(T v) {
_v = (unsigned int)(v % umod());
}
static_modint(bool v) { _v = ((unsigned int)(v) % umod()); }
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
mint& operator*=(const mint& rhs) {
unsigned long long z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
if (prime) {
assert(_v);
return pow(umod() - 2);
}
else {
auto eg = internal::inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool prime = internal::is_prime<m>;
};
template <int id> struct dynamic_modint : internal::modint_base {
using mint = dynamic_modint;
public:
static int mod() { return (int)(bt.umod()); }
static void set_mod(int m) {
assert(1 <= m);
bt = internal::barrett(m);
}
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
dynamic_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
dynamic_modint(T v) {
long long x = (long long)(v % (long long)(mod()));
if (x < 0) x += mod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
dynamic_modint(T v) {
_v = (unsigned int)(v % mod());
}
dynamic_modint(bool v) { _v = ((unsigned int)(v) % mod()); }
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v += mod() - rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator*=(const mint& rhs) {
_v = bt.mul(_v, rhs._v);
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
auto eg = internal::inv_gcd(_v, mod());
assert(eg.first == 1);
return eg.second;
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static internal::barrett bt;
static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt = 998244353;
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
namespace internal {
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};
template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
}
}
#endif
#ifndef ATCODER_CONVOLUTION_HPP
#define ATCODER_CONVOLUTION_HPP 1
#include <algorithm>
#include <array>
#include <cassert>
#include <type_traits>
#include <vector>
namespace atcoder {
namespace internal {
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly(std::vector<mint>& a) {
static constexpr int g = internal::primitive_root<mint::mod()>;
int n = int(a.size());
int h = internal::ceil_pow2(n);
static bool first = true;
static mint sum_e[30];
if (first) {
first = false;
mint es[30], ies[30];
int cnt2 = bsf(mint::mod() - 1);
mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
for (int i = cnt2; i >= 2; i--) {
// e^(2^i) == 1
es[i - 2] = e;
ies[i - 2] = ie;
e *= e;
ie *= ie;
}
mint now = 1;
for (int i = 0; i < cnt2 - 2; i++) {
sum_e[i] = es[i] * now;
now *= ies[i];
}
}
for (int ph = 1; ph <= h; ph++) {
int w = 1 << (ph - 1), p = 1 << (h - ph);
mint now = 1;
for (int s = 0; s < w; s++) {
int offset = s << (h - ph + 1);
for (int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p] * now;
a[i + offset] = l + r;
a[i + offset + p] = l - r;
}
now *= sum_e[bsf(~(unsigned int)(s))];
}
}
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly_inv(std::vector<mint>& a) {
static constexpr int g = internal::primitive_root<mint::mod()>;
int n = int(a.size());
int h = internal::ceil_pow2(n);
static bool first = true;
static mint sum_ie[30];
if (first) {
first = false;
mint es[30], ies[30];
int cnt2 = bsf(mint::mod() - 1);
mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
for (int i = cnt2; i >= 2; i--) {
// e^(2^i) == 1
es[i - 2] = e;
ies[i - 2] = ie;
e *= e;
ie *= ie;
}
mint now = 1;
for (int i = 0; i < cnt2 - 2; i++) {
sum_ie[i] = ies[i] * now;
now *= es[i];
}
}
for (int ph = h; ph >= 1; ph--) {
int w = 1 << (ph - 1), p = 1 << (h - ph);
mint inow = 1;
for (int s = 0; s < w; s++) {
int offset = s << (h - ph + 1);
for (int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p];
a[i + offset] = l + r;
a[i + offset + p] =
(unsigned long long)(mint::mod() + l.val() - r.val()) *
inow.val();
}
inow *= sum_ie[bsf(~(unsigned int)(s))];
}
}
}
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution(std::vector<mint> a, std::vector<mint> b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
if (std::min(n, m) <= 60) {
if (n < m) {
std::swap(n, m);
std::swap(a, b);
}
std::vector<mint> ans(n + m - 1);
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
ans[i + j] += a[i] * b[j];
}
}
return ans;
}
int z = 1 << internal::ceil_pow2(n + m - 1);
a.resize(z);
internal::butterfly(a);
b.resize(z);
internal::butterfly(b);
for (int i = 0; i < z; i++) {
a[i] *= b[i];
}
internal::butterfly_inv(a);
a.resize(n + m - 1);
mint iz = mint(z).inv();
for (int i = 0; i < n + m - 1; i++) a[i] *= iz;
return a;
}
template <unsigned int mod = 998244353,
class T,
std::enable_if_t<internal::is_integral<T>::value>* = nullptr>
std::vector<T> convolution(const std::vector<T>& a, const std::vector<T>& b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
using mint = static_modint<mod>;
std::vector<mint> a2(n), b2(m);
for (int i = 0; i < n; i++) {
a2[i] = mint(a[i]);
}
for (int i = 0; i < m; i++) {
b2[i] = mint(b[i]);
}
auto c2 = convolution(move(a2), move(b2));
std::vector<T> c(n + m - 1);
for (int i = 0; i < n + m - 1; i++) {
c[i] = c2[i].val();
}
return c;
}
std::vector<long long> convolution_ll(const std::vector<long long>& a,
const std::vector<long long>& b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
static constexpr unsigned long long MOD1 = 754974721;
static constexpr unsigned long long MOD2 = 167772161;
static constexpr unsigned long long MOD3 = 469762049;
static constexpr unsigned long long M2M3 = MOD2 * MOD3;
static constexpr unsigned long long M1M3 = MOD1 * MOD3;
static constexpr unsigned long long M1M2 = MOD1 * MOD2;
static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;
static constexpr unsigned long long i1 =
internal::inv_gcd(MOD2 * MOD3, MOD1).second;
static constexpr unsigned long long i2 =
internal::inv_gcd(MOD1 * MOD3, MOD2).second;
static constexpr unsigned long long i3 =
internal::inv_gcd(MOD1 * MOD2, MOD3).second;
auto c1 = convolution<MOD1>(a, b);
auto c2 = convolution<MOD2>(a, b);
auto c3 = convolution<MOD3>(a, b);
std::vector<long long> c(n + m - 1);
for (int i = 0; i < n + m - 1; i++) {
unsigned long long x = 0;
x += (c1[i] * i1) % MOD1 * M2M3;
x += (c2[i] * i2) % MOD2 * M1M3;
x += (c3[i] * i3) % MOD3 * M1M2;
long long diff =
c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1));
if (diff < 0) diff += MOD1;
static constexpr unsigned long long offset[5] = {
0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3 };
x -= offset[diff % 5];
c[i] = x;
}
return c;
}
}
#endif
#ifndef ATCODER_DSU_HPP
#define ATCODER_DSU_HPP 1
#include <algorithm>
#include <cassert>
#include <vector>
namespace atcoder {
struct dsu {
public:
dsu() : _n(0) {}
dsu(int n) : _n(n), parent_or_size(n, -1) {}
int merge(int a, int b) {
assert(0 <= a && a < _n);
assert(0 <= b && b < _n);
int x = leader(a), y = leader(b);
if (x == y) return x;
if (-parent_or_size[x] < -parent_or_size[y]) std::swap(x, y);
parent_or_size[x] += parent_or_size[y];
parent_or_size[y] = x;
return x;
}
bool same(int a, int b) {
assert(0 <= a && a < _n);
assert(0 <= b && b < _n);
return leader(a) == leader(b);
}
int leader(int a) {
assert(0 <= a && a < _n);
if (parent_or_size[a] < 0) return a;
return parent_or_size[a] = leader(parent_or_size[a]);
}
int size(int a) {
assert(0 <= a && a < _n);
return -parent_or_size[leader(a)];
}
std::vector<std::vector<int>> groups() {
std::vector<int> leader_buf(_n), group_size(_n);
for (int i = 0; i < _n; i++) {
leader_buf[i] = leader(i);
group_size[leader_buf[i]]++;
}
std::vector<std::vector<int>> result(_n);
for (int i = 0; i < _n; i++) {
result[i].reserve(group_size[i]);
}
for (int i = 0; i < _n; i++) {
result[leader_buf[i]].push_back(i);
}
result.erase(
std::remove_if(result.begin(), result.end(),
[&](const std::vector<int>& v) { return v.empty(); }),
result.end());
return result;
}
private:
int _n;
std::vector<int> parent_or_size;
};
}
#endif
#ifndef ATCODER_FENWICKTREE_HPP
#define ATCODER_FENWICKTREE_HPP 1
#include <cassert>
#include <vector>
namespace atcoder {
template <class T> struct fenwick_tree {
using U = internal::to_unsigned_t<T>;
public:
fenwick_tree() : _n(0) {}
fenwick_tree(int n) : _n(n), data(n) {}
void add(int p, T x) {
assert(0 <= p && p < _n);
p++;
while (p <= _n) {
data[p - 1] += U(x);
p += p & -p;
}
}
T sum(int l, int r) {
assert(0 <= l && l <= r && r <= _n);
return sum(r) - sum(l);
}
private:
int _n;
std::vector<U> data;
U sum(int r) {
U s = 0;
while (r > 0) {
s += data[r - 1];
r -= r & -r;
}
return s;
}
};
}
#endif
#ifndef ATCODER_LAZYSEGTREE_HPP
#define ATCODER_LAZYSEGTREE_HPP 1
#include <algorithm>
#include <cassert>
#include <iostream>
#include <vector>
namespace atcoder {
template <class S,
S(*op)(S, S),
S(*e)(),
class F,
S(*mapping)(F, S),
F(*composition)(F, F),
F(*id)()>
struct lazy_segtree {
public:
lazy_segtree() : lazy_segtree(0) {}
lazy_segtree(int n) : lazy_segtree(std::vector<S>(n, e())) {}
lazy_segtree(const std::vector<S>& v) : _n(int(v.size())) {
log = internal::ceil_pow2(_n);
size = 1 << log;
d = std::vector<S>(2 * size, e());
lz = std::vector<F>(size, id());
for (int i = 0; i < _n; i++) d[size + i] = v[i];
for (int i = size - 1; i >= 1; i--) {
update(i);
}
}
void set(int p, S x) {
assert(0 <= p && p < _n);
p += size;
for (int i = log; i >= 1; i--) push(p >> i);
d[p] = x;
for (int i = 1; i <= log; i++) update(p >> i);
}
S get(int p) {
assert(0 <= p && p < _n);
p += size;
for (int i = log; i >= 1; i--) push(p >> i);
return d[p];
}
S prod(int l, int r) {
assert(0 <= l && l <= r && r <= _n);
if (l == r) return e();
l += size;
r += size;
for (int i = log; i >= 1; i--) {
if (((l >> i) << i) != l) push(l >> i);
if (((r >> i) << i) != r) push(r >> i);
}
S sml = e(), smr = e();
while (l < r) {
if (l & 1) sml = op(sml, d[l++]);
if (r & 1) smr = op(d[--r], smr);
l >>= 1;
r >>= 1;
}
return op(sml, smr);
}
S all_prod() { return d[1]; }
void apply(int p, F f) {
assert(0 <= p && p < _n);
p += size;
for (int i = log; i >= 1; i--) push(p >> i);
d[p] = mapping(f, d[p]);
for (int i = 1; i <= log; i++) update(p >> i);
}
void apply(int l, int r, F f) {
assert(0 <= l && l <= r && r <= _n);
if (l == r) return;
l += size;
r += size;
for (int i = log; i >= 1; i--) {
if (((l >> i) << i) != l) push(l >> i);
if (((r >> i) << i) != r) push((r - 1) >> i);
}
{
int l2 = l, r2 = r;
while (l < r) {
if (l & 1) all_apply(l++, f);
if (r & 1) all_apply(--r, f);
l >>= 1;
r >>= 1;
}
l = l2;
r = r2;
}
for (int i = 1; i <= log; i++) {
if (((l >> i) << i) != l) update(l >> i);
if (((r >> i) << i) != r) update((r - 1) >> i);
}
}
template <bool (*g)(S)> int max_right(int l) {
return max_right(l, [](S x) { return g(x); });
}
template <class G> int max_right(int l, G g) {
assert(0 <= l && l <= _n);
assert(g(e()));
if (l == _n) return _n;
l += size;
for (int i = log; i >= 1; i--) push(l >> i);
S sm = e();
do {
while (l % 2 == 0) l >>= 1;
if (!g(op(sm, d[l]))) {
while (l < size) {
push(l);
l = (2 * l);
if (g(op(sm, d[l]))) {
sm = op(sm, d[l]);
l++;
}
}
return l - size;
}
sm = op(sm, d[l]);
l++;
} while ((l & -l) != l);
return _n;
}
template <bool (*g)(S)> int min_left(int r) {
return min_left(r, [](S x) { return g(x); });
}
template <class G> int min_left(int r, G g) {
assert(0 <= r && r <= _n);
assert(g(e()));
if (r == 0) return 0;
r += size;
for (int i = log; i >= 1; i--) push((r - 1) >> i);
S sm = e();
do {
r--;
while (r > 1 && (r % 2)) r >>= 1;
if (!g(op(d[r], sm))) {
while (r < size) {
push(r);
r = (2 * r + 1);
if (g(op(d[r], sm))) {
sm = op(d[r], sm);
r--;
}
}
return r + 1 - size;
}
sm = op(d[r], sm);
} while ((r & -r) != r);
return 0;
}
private:
int _n, size, log;
std::vector<S> d;
std::vector<F> lz;
void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
void all_apply(int k, F f) {
d[k] = mapping(f, d[k]);
if (k < size) lz[k] = composition(f, lz[k]);
}
void push(int k) {
all_apply(2 * k, lz[k]);
all_apply(2 * k + 1, lz[k]);
lz[k] = id();
}
};
}
#endif
#ifndef ATCODER_MATH_HPP
#define ATCODER_MATH_HPP 1
#include <algorithm>
#include <cassert>
#include <tuple>
#include <vector>
namespace atcoder {
long long pow_mod(long long x, long long n, int m) {
assert(0 <= n && 1 <= m);
if (m == 1) return 0;
internal::barrett bt((unsigned int)(m));
unsigned int r = 1, y = (unsigned int)(internal::safe_mod(x, m));
while (n) {
if (n & 1) r = bt.mul(r, y);
y = bt.mul(y, y);
n >>= 1;
}
return r;
}
long long inv_mod(long long x, long long m) {
assert(1 <= m);
auto z = internal::inv_gcd(x, m);
assert(z.first == 1);
return z.second;
}
std::pair<long long, long long> crt(const std::vector<long long>& r,
const std::vector<long long>& m) {
assert(r.size() == m.size());
int n = int(r.size());
long long r0 = 0, m0 = 1;
for (int i = 0; i < n; i++) {
assert(1 <= m[i]);
long long r1 = internal::safe_mod(r[i], m[i]), m1 = m[i];
if (m0 < m1) {
std::swap(r0, r1);
std::swap(m0, m1);
}
if (m0 % m1 == 0) {
if (r0 % m1 != r1) return { 0, 0 };
continue;
}
long long g, im;
std::tie(g, im) = internal::inv_gcd(m0, m1);
long long u1 = (m1 / g);
if ((r1 - r0) % g) return { 0, 0 };
long long x = (r1 - r0) / g % u1 * im % u1;
r0 += x * m0;
m0 *= u1;
if (r0 < 0) r0 += m0;
}
return { r0, m0 };
}
long long floor_sum(long long n, long long m, long long a, long long b) {
long long ans = 0;
if (a >= m) {
ans += (n - 1) * n * (a / m) / 2;
a %= m;
}
if (b >= m) {
ans += n * (b / m);
b %= m;
}
long long y_max = (a * n + b) / m, x_max = (y_max * m - b);
if (y_max == 0) return ans;
ans += (n - (x_max + a - 1) / a) * y_max;
ans += floor_sum(y_max, a, m, (a - x_max % a) % a);
return ans;
}
}
#endif
#ifndef ATCODER_MAXFLOW_HPP
#define ATCODER_MAXFLOW_HPP 1
#include <algorithm>
#include <cassert>
#include <limits>
#include <queue>
#include <vector>
namespace atcoder {
template <class Cap> struct mf_graph {
public:
mf_graph() : _n(0) {}
mf_graph(int n) : _n(n), g(n) {}
int add_edge(int from, int to, Cap cap) {
assert(0 <= from && from < _n);
assert(0 <= to && to < _n);
assert(0 <= cap);
int m = int(pos.size());
pos.push_back({ from, int(g[from].size()) });
g[from].push_back(_edge{ to, int(g[to].size()), cap });
g[to].push_back(_edge{ from, int(g[from].size()) - 1, 0 });
return m;
}
struct edge {
int from, to;
Cap cap, flow;
};
edge get_edge(int i) {
int m = int(pos.size());
assert(0 <= i && i < m);
auto _e = g[pos[i].first][pos[i].second];
auto _re = g[_e.to][_e.rev];
return edge{ pos[i].first, _e.to, _e.cap + _re.cap, _re.cap };
}
std::vector<edge> edges() {
int m = int(pos.size());
std::vector<edge> result;
for (int i = 0; i < m; i++) {
result.push_back(get_edge(i));
}
return result;
}
void change_edge(int i, Cap new_cap, Cap new_flow) {
int m = int(pos.size());
assert(0 <= i && i < m);
assert(0 <= new_flow && new_flow <= new_cap);
auto& _e = g[pos[i].first][pos[i].second];
auto& _re = g[_e.to][_e.rev];
_e.cap = new_cap - new_flow;
_re.cap = new_flow;
}
Cap flow(int s, int t) {
return flow(s, t, std::numeric_limits<Cap>::max());
}
Cap flow(int s, int t, Cap flow_limit) {
assert(0 <= s && s < _n);
assert(0 <= t && t < _n);
std::vector<int> level(_n), iter(_n);
internal::simple_queue<int> que;
auto bfs = [&]() {
std::fill(level.begin(), level.end(), -1);
level[s] = 0;
que.clear();
que.push(s);
while (!que.empty()) {
int v = que.front();
que.pop();
for (auto e : g[v]) {
if (e.cap == 0 || level[e.to] >= 0) continue;
level[e.to] = level[v] + 1;
if (e.to == t) return;
que.push(e.to);
}
}
};
auto dfs = [&](auto self, int v, Cap up) {
if (v == s) return up;
Cap res = 0;
int level_v = level[v];
for (int& i = iter[v]; i < int(g[v].size()); i++) {
_edge& e = g[v][i];
if (level_v <= level[e.to] || g[e.to][e.rev].cap == 0) continue;
Cap d =
self(self, e.to, std::min(up - res, g[e.to][e.rev].cap));
if (d <= 0) continue;
g[v][i].cap += d;
g[e.to][e.rev].cap -= d;
res += d;
if (res == up) break;
}
return res;
};
Cap flow = 0;
while (flow < flow_limit) {
bfs();
if (level[t] == -1) break;
std::fill(iter.begin(), iter.end(), 0);
while (flow < flow_limit) {
Cap f = dfs(dfs, t, flow_limit - flow);
if (!f) break;
flow += f;
}
}
return flow;
}
std::vector<bool> min_cut(int s) {
std::vector<bool> visited(_n);
internal::simple_queue<int> que;
que.push(s);
while (!que.empty()) {
int p = que.front();
que.pop();
visited[p] = true;
for (auto e : g[p]) {
if (e.cap && !visited[e.to]) {
visited[e.to] = true;
que.push(e.to);
}
}
}
return visited;
}
private:
int _n;
struct _edge {
int to, rev;
Cap cap;
};
std::vector<std::pair<int, int>> pos;
std::vector<std::vector<_edge>> g;
};
}
#endif
#ifndef ATCODER_MINCOSTFLOW_HPP
#define ATCODER_MINCOSTFLOW_HPP 1
#include <algorithm>
#include <cassert>
#include <limits>
#include <queue>
#include <vector>
namespace atcoder {
template <class Cap, class Cost> struct mcf_graph {
public:
mcf_graph() {}
mcf_graph(int n) : _n(n), g(n) {}
int add_edge(int from, int to, Cap cap, Cost cost) {
assert(0 <= from && from < _n);
assert(0 <= to && to < _n);
int m = int(pos.size());
pos.push_back({ from, int(g[from].size()) });
g[from].push_back(_edge{ to, int(g[to].size()), cap, cost });
g[to].push_back(_edge{ from, int(g[from].size()) - 1, 0, -cost });
return m;
}
struct edge {
int from, to;
Cap cap, flow;
Cost cost;
};
edge get_edge(int i) {
int m = int(pos.size());
assert(0 <= i && i < m);
auto _e = g[pos[i].first][pos[i].second];
auto _re = g[_e.to][_e.rev];
return edge{
pos[i].first, _e.to, _e.cap + _re.cap, _re.cap, _e.cost,
};
}
std::vector<edge> edges() {
int m = int(pos.size());
std::vector<edge> result(m);
for (int i = 0; i < m; i++) {
result[i] = get_edge(i);
}
return result;
}
std::pair<Cap, Cost> flow(int s, int t) {
return flow(s, t, std::numeric_limits<Cap>::max());
}
std::pair<Cap, Cost> flow(int s, int t, Cap flow_limit) {
return slope(s, t, flow_limit).back();
}
std::vector<std::pair<Cap, Cost>> slope(int s, int t) {
return slope(s, t, std::numeric_limits<Cap>::max());
}
std::vector<std::pair<Cap, Cost>> slope(int s, int t, Cap flow_limit) {
assert(0 <= s && s < _n);
assert(0 <= t && t < _n);
assert(s != t);
std::vector<Cost> dual(_n, 0), dist(_n);
std::vector<int> pv(_n), pe(_n);
std::vector<bool> vis(_n);
auto dual_ref = [&]() {
std::fill(dist.begin(), dist.end(),
std::numeric_limits<Cost>::max());
std::fill(pv.begin(), pv.end(), -1);
std::fill(pe.begin(), pe.end(), -1);
std::fill(vis.begin(), vis.end(), false);
struct Q {
Cost key;
int to;
bool operator<(Q r) const { return key > r.key; }
};
std::priority_queue<Q> que;
dist[s] = 0;
que.push(Q{ 0, s });
while (!que.empty()) {
int v = que.top().to;
que.pop();
if (vis[v]) continue;
vis[v] = true;
if (v == t) break;
for (int i = 0; i < int(g[v].size()); i++) {
auto e = g[v][i];
if (vis[e.to] || !e.cap) continue;
Cost cost = e.cost - dual[e.to] + dual[v];
if (dist[e.to] - dist[v] > cost) {
dist[e.to] = dist[v] + cost;
pv[e.to] = v;
pe[e.to] = i;
que.push(Q{ dist[e.to], e.to });
}
}
}
if (!vis[t]) {
return false;
}
for (int v = 0; v < _n; v++) {
if (!vis[v]) continue;
dual[v] -= dist[t] - dist[v];
}
return true;
};
Cap flow = 0;
Cost cost = 0, prev_cost = -1;
std::vector<std::pair<Cap, Cost>> result;
result.push_back({ flow, cost });
while (flow < flow_limit) {
if (!dual_ref()) break;
Cap c = flow_limit - flow;
for (int v = t; v != s; v = pv[v]) {
c = std::min(c, g[pv[v]][pe[v]].cap);
}
for (int v = t; v != s; v = pv[v]) {
auto& e = g[pv[v]][pe[v]];
e.cap -= c;
g[v][e.rev].cap += c;
}
Cost d = -dual[s];
flow += c;
cost += c * d;
if (prev_cost == d) {
result.pop_back();
}
result.push_back({ flow, cost });
prev_cost = cost;
}
return result;
}
private:
int _n;
struct _edge {
int to, rev;
Cap cap;
Cost cost;
};
std::vector<std::pair<int, int>> pos;
std::vector<std::vector<_edge>> g;
};
}
#endif
#ifndef ATCODER_SCC_HPP
#define ATCODER_SCC_HPP 1
#include <algorithm>
#include <cassert>
#include <vector>
namespace atcoder {
struct scc_graph {
public:
scc_graph() : internal(0) {}
scc_graph(int n) : internal(n) {}
void add_edge(int from, int to) {
int n = internal.num_vertices();
assert(0 <= from && from < n);
assert(0 <= to && to < n);
internal.add_edge(from, to);
}
std::vector<std::vector<int>> scc() { return internal.scc(); }
private:
internal::scc_graph internal;
};
}
#endif
#ifndef ATCODER_SEGTREE_HPP
#define ATCODER_SEGTREE_HPP 1
#include <algorithm>
#include <cassert>
#include <vector>
namespace atcoder {
template <class S, S(*op)(S, S), S(*e)()> struct segtree {
public:
segtree() : segtree(0) {}
segtree(int n) : segtree(std::vector<S>(n, e())) {}
segtree(const std::vector<S>& v) : _n(int(v.size())) {
log = internal::ceil_pow2(_n);
size = 1 << log;
d = std::vector<S>(2 * size, e());
for (int i = 0; i < _n; i++) d[size + i] = v[i];
for (int i = size - 1; i >= 1; i--) {
update(i);
}
}
void set(int p, S x) {
assert(0 <= p && p < _n);
p += size;
d[p] = x;
for (int i = 1; i <= log; i++) update(p >> i);
}
S get(int p) {
assert(0 <= p && p < _n);
return d[p + size];
}
S prod(int l, int r) {
assert(0 <= l && l <= r && r <= _n);
S sml = e(), smr = e();
l += size;
r += size;
while (l < r) {
if (l & 1) sml = op(sml, d[l++]);
if (r & 1) smr = op(d[--r], smr);
l >>= 1;
r >>= 1;
}
return op(sml, smr);
}
S all_prod() { return d[1]; }
template <bool (*f)(S)> int max_right(int l) {
return max_right(l, [](S x) { return f(x); });
}
template <class F> int max_right(int l, F f) {
assert(0 <= l && l <= _n);
assert(f(e()));
if (l == _n) return _n;
l += size;
S sm = e();
do {
while (l % 2 == 0) l >>= 1;
if (!f(op(sm, d[l]))) {
while (l < size) {
l = (2 * l);
if (f(op(sm, d[l]))) {
sm = op(sm, d[l]);
l++;
}
}
return l - size;
}
sm = op(sm, d[l]);
l++;
} while ((l & -l) != l);
return _n;
}
template <bool (*f)(S)> int min_left(int r) {
return min_left(r, [](S x) { return f(x); });
}
template <class F> int min_left(int r, F f) {
assert(0 <= r && r <= _n);
assert(f(e()));
if (r == 0) return 0;
r += size;
S sm = e();
do {
r--;
while (r > 1 && (r % 2)) r >>= 1;
if (!f(op(d[r], sm))) {
while (r < size) {
r = (2 * r + 1);
if (f(op(d[r], sm))) {
sm = op(d[r], sm);
r--;
}
}
return r + 1 - size;
}
sm = op(d[r], sm);
} while ((r & -r) != r);
return 0;
}
private:
int _n, size, log;
std::vector<S> d;
void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
};
}
#endif
#ifndef ATCODER_STRING_HPP
#define ATCODER_STRING_HPP 1
#include <algorithm>
#include <cassert>
#include <numeric>
#include <string>
#include <vector>
namespace atcoder {
namespace internal {
std::vector<int> sa_naive(const std::vector<int>& s) {
int n = int(s.size());
std::vector<int> sa(n);
std::iota(sa.begin(), sa.end(), 0);
std::sort(sa.begin(), sa.end(), [&](int l, int r) {
if (l == r) return false;
while (l < n && r < n) {
if (s[l] != s[r]) return s[l] < s[r];
l++;
r++;
}
return l == n;
});
return sa;
}
std::vector<int> sa_doubling(const std::vector<int>& s) {
int n = int(s.size());
std::vector<int> sa(n), rnk = s, tmp(n);
std::iota(sa.begin(), sa.end(), 0);
for (int k = 1; k < n; k *= 2) {
auto cmp = [&](int x, int y) {
if (rnk[x] != rnk[y]) return rnk[x] < rnk[y];
int rx = x + k < n ? rnk[x + k] : -1;
int ry = y + k < n ? rnk[y + k] : -1;
return rx < ry;
};
std::sort(sa.begin(), sa.end(), cmp);
tmp[sa[0]] = 0;
for (int i = 1; i < n; i++) {
tmp[sa[i]] = tmp[sa[i - 1]] + (cmp(sa[i - 1], sa[i]) ? 1 : 0);
}
std::swap(tmp, rnk);
}
return sa;
}
template <int THRESHOLD_NAIVE = 10, int THRESHOLD_DOUBLING = 40>
std::vector<int> sa_is(const std::vector<int>& s, int upper) {
int n = int(s.size());
if (n == 0) return {};
if (n == 1) return { 0 };
if (n == 2) {
if (s[0] < s[1]) {
return { 0, 1 };
}
else {
return { 1, 0 };
}
}
if (n < THRESHOLD_NAIVE) {
return sa_naive(s);
}
if (n < THRESHOLD_DOUBLING) {
return sa_doubling(s);
}
std::vector<int> sa(n);
std::vector<bool> ls(n);
for (int i = n - 2; i >= 0; i--) {
ls[i] = (s[i] == s[i + 1]) ? ls[i + 1] : (s[i] < s[i + 1]);
}
std::vector<int> sum_l(upper + 1), sum_s(upper + 1);
for (int i = 0; i < n; i++) {
if (!ls[i]) {
sum_s[s[i]]++;
}
else {
sum_l[s[i] + 1]++;
}
}
for (int i = 0; i <= upper; i++) {
sum_s[i] += sum_l[i];
if (i < upper) sum_l[i + 1] += sum_s[i];
}
auto induce = [&](const std::vector<int>& lms) {
std::fill(sa.begin(), sa.end(), -1);
std::vector<int> buf(upper + 1);
std::copy(sum_s.begin(), sum_s.end(), buf.begin());
for (auto d : lms) {
if (d == n) continue;
sa[buf[s[d]]++] = d;
}
std::copy(sum_l.begin(), sum_l.end(), buf.begin());
sa[buf[s[n - 1]]++] = n - 1;
for (int i = 0; i < n; i++) {
int v = sa[i];
if (v >= 1 && !ls[v - 1]) {
sa[buf[s[v - 1]]++] = v - 1;
}
}
std::copy(sum_l.begin(), sum_l.end(), buf.begin());
for (int i = n - 1; i >= 0; i--) {
int v = sa[i];
if (v >= 1 && ls[v - 1]) {
sa[--buf[s[v - 1] + 1]] = v - 1;
}
}
};
std::vector<int> lms_map(n + 1, -1);
int m = 0;
for (int i = 1; i < n; i++) {
if (!ls[i - 1] && ls[i]) {
lms_map[i] = m++;
}
}
std::vector<int> lms;
lms.reserve(m);
for (int i = 1; i < n; i++) {
if (!ls[i - 1] && ls[i]) {
lms.push_back(i);
}
}
induce(lms);
if (m) {
std::vector<int> sorted_lms;
sorted_lms.reserve(m);
for (int v : sa) {
if (lms_map[v] != -1) sorted_lms.push_back(v);
}
std::vector<int> rec_s(m);
int rec_upper = 0;
rec_s[lms_map[sorted_lms[0]]] = 0;
for (int i = 1; i < m; i++) {
int l = sorted_lms[i - 1], r = sorted_lms[i];
int end_l = (lms_map[l] + 1 < m) ? lms[lms_map[l] + 1] : n;
int end_r = (lms_map[r] + 1 < m) ? lms[lms_map[r] + 1] : n;
bool same = true;
if (end_l - l != end_r - r) {
same = false;
}
else {
while (l < end_l) {
if (s[l] != s[r]) {
break;
}
l++;
r++;
}
if (l == n || s[l] != s[r]) same = false;
}
if (!same) rec_upper++;
rec_s[lms_map[sorted_lms[i]]] = rec_upper;
}
auto rec_sa =
sa_is<THRESHOLD_NAIVE, THRESHOLD_DOUBLING>(rec_s, rec_upper);
for (int i = 0; i < m; i++) {
sorted_lms[i] = lms[rec_sa[i]];
}
induce(sorted_lms);
}
return sa;
}
}
std::vector<int> suffix_array(const std::vector<int>& s, int upper) {
assert(0 <= upper);
for (int d : s) {
assert(0 <= d && d <= upper);
}
auto sa = internal::sa_is(s, upper);
return sa;
}
template <class T> std::vector<int> suffix_array(const std::vector<T>& s) {
int n = int(s.size());
std::vector<int> idx(n);
iota(idx.begin(), idx.end(), 0);
sort(idx.begin(), idx.end(), [&](int l, int r) { return s[l] < s[r]; });
std::vector<int> s2(n);
int now = 0;
for (int i = 0; i < n; i++) {
if (i && s[idx[i - 1]] != s[idx[i]]) now++;
s2[idx[i]] = now;
}
return internal::sa_is(s2, now);
}
std::vector<int> suffix_array(const std::string& s) {
int n = int(s.size());
std::vector<int> s2(n);
for (int i = 0; i < n; i++) {
s2[i] = s[i];
}
return internal::sa_is(s2, 255);
}
template <class T>
std::vector<int> lcp_array(const std::vector<T>& s,
const std::vector<int>& sa) {
int n = int(s.size());
assert(n >= 1);
std::vector<int> rnk(n);
for (int i = 0; i < n; i++) {
rnk[sa[i]] = i;
}
std::vector<int> lcp(n - 1);
int h = 0;
for (int i = 0; i < n; i++) {
if (h > 0) h--;
if (rnk[i] == 0) continue;
int j = sa[rnk[i] - 1];
for (; j + h < n && i + h < n; h++) {
if (s[j + h] != s[i + h]) break;
}
lcp[rnk[i] - 1] = h;
}
return lcp;
}
std::vector<int> lcp_array(const std::string& s, const std::vector<int>& sa) {
int n = int(s.size());
std::vector<int> s2(n);
for (int i = 0; i < n; i++) {
s2[i] = s[i];
}
return lcp_array(s2, sa);
}
template <class T> std::vector<int> z_algorithm(const std::vector<T>& s) {
int n = int(s.size());
if (n == 0) return {};
std::vector<int> z(n);
z[0] = 0;
for (int i = 1, j = 0; i < n; i++) {
int& k = z[i];
k = (j + z[j] <= i) ? 0 : std::min(j + z[j] - i, z[i - j]);
while (i + k < n && s[k] == s[i + k]) k++;
if (j + z[j] < i + z[i]) j = i;
}
z[0] = n;
return z;
}
std::vector<int> z_algorithm(const std::string& s) {
int n = int(s.size());
std::vector<int> s2(n);
for (int i = 0; i < n; i++) {
s2[i] = s[i];
}
return z_algorithm(s2);
}
}
#endif
#ifndef ATCODER_TWOSAT_HPP
#define ATCODER_TWOSAT_HPP 1
#include <cassert>
#include <vector>
namespace atcoder {
struct two_sat {
public:
two_sat() : _n(0), scc(0) {}
two_sat(int n) : _n(n), _answer(n), scc(2 * n) {}
void add_clause(int i, bool f, int j, bool g) {
assert(0 <= i && i < _n);
assert(0 <= j && j < _n);
scc.add_edge(2 * i + (f ? 0 : 1), 2 * j + (g ? 1 : 0));
scc.add_edge(2 * j + (g ? 0 : 1), 2 * i + (f ? 1 : 0));
}
bool satisfiable() {
auto id = scc.scc_ids().second;
for (int i = 0; i < _n; i++) {
if (id[2 * i] == id[2 * i + 1]) return false;
_answer[i] = id[2 * i] < id[2 * i + 1];
}
return true;
}
std::vector<bool> answer() { return _answer; }
private:
int _n;
std::vector<bool> _answer;
internal::scc_graph scc;
};
}
#endif
//ACL end
#pragma warning(disable:4996)
#include <bits/stdc++.h>
using namespace std;
using namespace atcoder;
using mint = static_modint<1000000007>;
using vmint = vector<mint>;
using vvmint = vector<vmint>;
using vvvmint = vector<vvmint>;
using vvvvmint = vector<vvvmint>;
istream& operator>>(istream& is, mint& a) {
long long v;
is >> v;
a = v;
return is;
}
ostream& operator<<(ostream& os, mint a) {
return os << a.val();
}
#ifdef _MSC_VER
#include <intrin.h>
#define __builtin_popcount __popcnt
#define __builtin_popcountll __popcnt64
#endif
template<typename T>
using vec = vector<T>;
using ll = long long;
using ull = unsigned long long;
using stirng = string;
using itn = int;
using vs = vec<string>;
using vc = vec<char>;
using vvc = vec<vc>;
using vvvc = vec<vvc>;
using vi = vec<int>;
using vvi = vec<vi>;
using vvvi = vec<vvi>;
using vvvvi = vec<vvvi>;
using vll = vec<ll>;
using vvll = vec<vll>;
using vvvll = vec<vvll>;
using vvvvll = vec<vvvll>;
using si = set<int>;
using vsi = vec<si>;
using vvsi = vec<vsi>;
using vvvsi = vec<vvsi>;
using sll = set<ll>;
using vsll = vec<sll>;
using vvsll = vec<vsll>;
using vvvsll = vec<vvsll>;
using vd = vec<double>;
using vvd = vec<vd>;
using vvvd = vec<vvd>;
using vvvvd = vec<vvvd>;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pd = pair<double, double>;
using mii = map<int, int>;
using mll = map<ll, ll>;
using msi = multiset<int>;
using msll = multiset<ll>;
using vpii = vec<pii>;
using vvpii = vec<vpii>;
using vvvpii = vec<vvpii>;
using vpll = vec<pll>;
using vvpll = vec<vpll>;
using vvvpll = vec<vvpll>;
using vpd = vec<pd>;
using spii = set<pii>;
using spll = set<pll>;
using spd = set<pd>;
using vspll = vec<spll>;
using vvspll = vec<vspll>;
using vb = vec<bool>;
using vvb = vec<vb>;
using vvvb = vec<vvb>;
#define rep(i,j,n) for(ll i=j;i<(n);i++)
#define rrep(i,j,n) for (ll i = (n)-1; i >=j; i--)
#define Call_4th(_1, _2, _3, _4, ...) _4
#define rp(...) Call_4th(__VA_ARGS__, _1, rp2)(__VA_ARGS__)
#define rp2(i, n) rep(i, 0, n)
#define rrp(i,n) rrep(i,0,(n))
#define all(v) v.begin(), v.end()
#define pb push_back
#define pp pop_back()
#define bk back()
#define ins insert
#define yes cout<<"Yes"<<endl;
#define no cout<<"No"<<endl;
#define NL {cout<<endl;}
#define n0 {cout<<"-1"<<endl;}
#define lwb lower_bound
#define upb upper_bound
#define reutrn return
#define Endl endl
template<typename T>
int len(T& x) { return int(x.size()); }
#define sz size()
#define fi first
#define se second
#define nxp next_permutation
ll mod0 = 998244353, lmax = 4e18, inf = 1050000000;
double pi = 3.141592653589793238462643;
//cin系統
template<typename... T>
void in(T&... X) { (cin >> ... >> X); }
template<typename T>
void ain(vec<T>& Y) { rp(K, Y.size()) cin >> Y[K]; }
template<typename T>
void ain(set<T>& Y, auto n) {
rp(i, n) {
T YY; cin >> YY;
Y.insert(YY);
}
}
template<typename T>
void ain(multiset<T>& Y, auto n) {
rp(i, n) {
T YY; cin >> YY;
Y.insert(YY);
}
}
template<typename T>
void ain(pair<T, T>& a) { cin >> a.fi >> a.se; }
template<typename T>
void bin(vec<T>& Z) { rp(L, Z.size()) ain(Z[L]); }
//cout系統
// vector
template <typename T> struct is_vector : false_type {};
template <typename T, typename Alloc>
struct is_vector<vector<T, Alloc>> : true_type {};
// queue
template <typename T> struct is_queue : false_type {};
template <typename T, typename Container>
struct is_queue<queue<T, Container>> : true_type {};
// stack
template <typename T> struct is_stack : false_type {};
template <typename T, typename Container>
struct is_stack<stack<T, Container>> : true_type {};
// pair
template <typename T> struct is_pair : false_type {};
template <typename T1, typename T2>
struct is_pair<pair<T1, T2>> : true_type {};
// set / multiset
template <typename T> struct is_set_like : false_type {};
template <typename Key, typename Compare, typename Alloc>
struct is_set_like<set<Key, Compare, Alloc>> : true_type {};
template <typename Key, typename Compare, typename Alloc>
struct is_set_like<multiset<Key, Compare, Alloc>> : true_type {};
// map / multimap
template <typename T> struct is_map_like : false_type {};
template <typename Key, typename Val, typename Compare, typename Alloc>
struct is_map_like<map<Key, Val, Compare, Alloc>> : true_type {};
template <typename Key, typename Val, typename Compare, typename Alloc>
struct is_map_like<multimap<Key, Val, Compare, Alloc>> : true_type {};
template <typename T>
void aout(const T& x) {
if constexpr (is_vector<T>::value) {
for (const auto& e : x) aout(e);
cout << endl;
}
else if constexpr (is_queue<T>::value) {
auto copy = x;
while (!copy.empty()) {
aout(copy.front());
copy.pop();
}
cout << endl;
}
else if constexpr (is_stack<T>::value) {
auto copy = x;
while (!copy.empty()) {
aout(copy.top());
copy.pop();
}
cout << endl;
}
else if constexpr (is_pair<T>::value) {
aout(x.first);
aout(x.second);
cout << endl;
}
else if constexpr (is_set_like<T>::value) {
for (const auto& e : x) aout(e);
cout << endl;
}
else if constexpr (is_map_like<T>::value) {
for (const auto& e : x) aout(e); // pair<const Key, Val>
cout << endl;
}
else {
cout << x << " ";
}
}
//数学系
ll modcnt(ll l, ll r, ll m, ll a) {//l以上r以下の整数iでi≡a(mod m)となるものの個数(l>r,a<0等も可)
assert(m != 0);
m = abs(m);
ll x = l + ((a - l) % m + m) % m;//l以上で最小のi≡a(mod m)となるi
if (x > r) return 0;
return (r - x) / m + 1;
}
ll dsum(ll a) {//桁和
ll r = 0;
while (a != 0) {
r += a % 10;
a /= 10;
}
return r;
}
ll dnum(ll a) {//桁数(0は0桁)
ll r = 0;
while (a != 0) {
r++;
a /= 10;
}
return r;
}
sll yk(ll n) {//約数全列挙O(sqrt(N)),set<int>
sll yaku;
for (ll i = 1; i * i <= n; i++) if (n % i == 0) {
yaku.insert(i);
yaku.insert(n / i);
}
return yaku;
}
vi ssa(int n) {//n:必要な素数の最大値 素数全列挙 線形篩
vector<int> prime;
vector<int>lpf(n + 1, 0);//最小素因数
rep(i, 2, n + 1) {
if (lpf[i] == 0) {
lpf[i] = i;
prime.push_back(i);
}
for (int k : prime) {
if (k * i > n || k > lpf[i]) break;//k最小素因数よりk<=i
lpf[k * i] = k;//kを最小素因数に持つ数k*iを拾う
}
}
return prime;
}
vector<pll> sib(ll x) {//素因数分解
if (x == 1) return vector<pll>(1, { 1,1 });
vector<pll> ans;
for (ll i = 2; i * i <= x; i++) {//rootx回iを回しxで割る
ll kaisu = 0;
while (x % i == 0) {
x /= i; kaisu++;
}
if (kaisu > 0) ans.pb({ i,kaisu });
}
if (x != 1) ans.pb({ x,1 });
return ans;
}
bool isp(ll x) {//素数判定 O(sqrt(x))
auto y = sib(x);
return (x != 1 && y.sz == 1 && y[0] == pll{ x, 1 });
}
vec<vec<pll>> sib(ll x, ll y) {//閉区間[x,y]全素因数分解 x=1は何も返さない O(max(sqrt(y),y-x)loglogy) ABC227G ABC412E
vi b = ssa(sqrt(y) + 100);
vec<vec<pll>> r(y - x + 1);
vll num(y - x + 1);
rp(i, y - x + 1) num[i] = x + i;
for (ll k : b) for (ll a = (1 + (x - 1) / k) * k; a <= y; a += k) {
ll kaisu = 0;
while (num[a - x] % k == 0) {
num[a - x] /= k; kaisu++;
}
if (kaisu) r[a - x].pb({ k,kaisu });
}
rp(i, y - x + 1) if (num[i] != 1) r[i].pb({ num[i],1 });
return r;
}
template<typename T>
ll sqrtll(T a) {//整数sqrt a<0orr非整数の場合-1を返す
if (a < 0) return -1;
ll r = sqrt(a);
while (r * r > a) r--;
while ((r + 1) * (r + 1) <= a) r++;
if (r * r == a)return r;
else return -1;
}
#define llsqrt sqrtll
ll powll(ll a, ll b) {//llでpow
ll c = 1;
assert(pow(a, b) <= 9e18);
rp(i, b) {
c *= a;
}
return c;
}
#define llpow powll
template<typename T>
T sq(T a) {//2乗
return a * a;
}
template<typename T>
T cb(T a) {//3乗
return a * a * a;
}
string basea(ll x, ll a) {//xをa進法に変換
string r;
while (x != 0) {
r.pb(x % a + '0');
x /= a;
}
reverse(all(r));
return r;
}
ll base10(string x, ll a) {//a進数のxを10進法に戻す
ll r = 0;
rp(i, x.sz) {
r *= a;
r += x[i] - '0';
}
return r;
}
vll vbasea(ll x, ll a) {//xをa進法に変換(vector)
vll r;
while (x != 0) {
r.pb(x % a);
x /= a;
}
reverse(all(r));
return r;
}
template<typename T>
ll bc(T x) {//bitcount
assert(x >= 0);
return __builtin_popcount(x);
}
double ds(double x1, double x2, double y1, double y2) {//dist
return sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
}
ll ds2(ll x1, ll x2, ll y1, ll y2) {//distの2乗(整数値)
return (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2);
}
template<typename T>
ll ds2(vec<T> a) {
return (a[0] - a[2]) * (a[0] - a[2]) + (a[1] - a[3]) * (a[1] - a[3]);
}
ll gpsum(ll a, ll r, ll n, ll m) {//初項a,公比r,項数nの等比数列の総和mod m r=10でレピュニットも可能
if (n == 0) return 0;
if (n == 1) return a % m;
modint::set_mod(m);
if (n % 2 == 1) return (a + gpsum(a * r % m, r, n - 1, m)) % m;
else return ((modint(r).pow(n / 2) + 1) * gpsum(a, r, n / 2, m)).val();
}
//二分探索
template<typename T>
auto lwa(typename std::vector<T>::iterator b, typename std::vector<T>::iterator e, T c) {//[b,e)でcより小さい最大の値のイテレータ(複数あれば右端)
auto it = std::lower_bound(b, e, c);
if (it == b) return e;
--it;
return it;
}
template<typename T>
auto lwa(vector<T>& a, T b) {//aでbより小さい最大の値のイテレータ(複数あれば右端)
return lwa(all(a), b);
}
template<typename T>
auto lwa(set<T>& a, T b) {//aでbより小さい最大の値のイテレータ(複数あれば右端)
auto i = a.lwb(b);
if (i == a.begin()) return a.end();
else i--;
return i;
}
template<typename T>
auto lwa(multiset<T>& a, T b) {//aでbより小さい最大の値のイテレータ(複数あれば右端)
auto i = a.lwb(b);
if (i == a.begin()) return a.end();
else i--;
return i;
}
template<typename T>
auto lwc(typename std::vector<T>::iterator b, typename std::vector<T>::iterator e, T c) {//aでb以下の最大の値のイテレータ(複数あれば左端)
auto i = lwb(b, e, c);
if (i != e && *i == c) return i;
if (i == b) return e;
else i--;
return i;
}
template<typename T>
auto lwc(vector<T>& a, T b) {//aでb以下の最大の値のイテレータ(複数あれば左端)
return lwc(all(a), b);
}
template<typename T>
auto lwc(set<T>& a, T b) {//aでb以下の最大の値のイテレータ(複数あれば左端)
auto i = a.lwb(b);
if (i != a.end() && *i == b) return i;
if (i == a.begin()) return a.end();
else i--;
return i;
}
template<typename T>
auto lwc(multiset<T>& a, T b) {//aでb以下の最大の値のイテレータ(複数あれば左端)
auto i = a.lwb(b);
if (i != a.end() && *i == b) return i;
if (i == a.begin()) return a.end();
else i--;
return i;
}
template <typename T>
std::pair<typename vector<T>::iterator, typename vector<T>::iterator> its(vec<T>& v, T a) {//{--lwb,lwb}({x未満の右端,x以上の左端})のpair返す(なければend())
auto it = lwb(all(v), a);
if (it == v.begin()) return { v.end(), it };
auto it2 = it; it2--;
return { it2,it };
}
template <typename T>
std::pair<typename set<T>::iterator, typename set<T>::iterator> its(set<T>& v, T a) {//{--lwb,lwb}({x未満の右端,x以上の左端})のpair返す(なければend())
auto it = v.lwb(a);
if (it == v.begin()) return { v.end(), it };
auto it2 = it; it2--;
return { it2,it };
}
template <typename T>
std::pair<typename multiset<T>::iterator, typename multiset<T>::iterator> its(multiset<T>& v, T a) {//{--lwb,lwb}({x未満の右端,x以上の左端})のpair返す(なければend())
auto it = v.lwb(a);
if (it == v.begin()) return { v.end(), it };
auto it2 = it; it2--;
return { it2,it };
}
template <typename T>
typename vector<T>::iterator nits(vec<T>& v, T a, bool isr = 1) {//itsのうちaに近い方返す(距離同じの場合isr==0なら左優先,1なら右優先) v.sz==0のときv.end()返す
auto cd = its(v, a);
if (cd.fi == v.end()) return cd.se;
if (cd.se == v.end()) return cd.fi;
auto l = a - *cd.fi, r = *cd.se - a;
if (l < r) return cd.fi;
if (l > r || isr == 1) return cd.se;
return cd.fi;
}
template <typename T>
typename set<T>::iterator nits(set<T>& v, T a, bool isr = 1) {//itsのうちaに近い方返す(距離同じの場合isr==0なら左優先,1なら右優先) v.sz==0のときv.end()返す
auto cd = its(v, a);
if (cd.fi == v.end()) return cd.se;
if (cd.se == v.end()) return cd.fi;
auto l = a - *cd.fi, r = *cd.se - a;
if (l < r) return cd.fi;
if (l > r || isr == 1) return cd.se;
return cd.fi;
}
template <typename T>
typename multiset<T>::iterator nits(multiset<T>& v, T a, bool isr = 1) {//itsのうちaに近い方返す(距離同じの場合isr==0なら左優先,1なら右優先) v.sz==0のときv.end()返す
auto cd = its(v, a);
if (cd.fi == v.end()) return cd.se;
if (cd.se == v.end()) return cd.fi;
auto l = a - *cd.fi, r = *cd.se - a;
if (l < r) return cd.fi;
if (l > r || isr == 1) return cd.se;
return cd.fi;
}
template <typename T>
int rcount(vec<T>& a, T l, T r) {//ソート済配列aから[l,r]の範囲(l以上r以下)の要素カウント
//右端を超える最小のi-左端に引っかかる最小のi
//l,rのどちらに対しても境界を含む/含まないを入れ替えるときupb/lwbを変えれば良い
return upb(all(a), r) - lwb(all(a), l);
}
template <typename T>
int rcount(set<T>& a, T l, T r) {//ソート済配列aから[l,r]の範囲(l以上r以下)の要素カウント
return a.upb(r) - a.lwb(l);
}
template <class Container, class Key>
bool has(const Container& c, const Key& x) {//sort済vector/set/map等に対しその値を持つかどうか返す
if constexpr (is_set_like<Container>::value || is_map_like<Container>::value) {
// set / multiset / map
return c.find(x) != c.end();
}
else {
// vector 等（ソート済前提）
return std::binary_search(c.begin(), c.end(), x);
}
}
//配列便利関数系
template<typename T>
bool chmin(T& M1, T M2) {
if (M1 > M2) { M1 = M2; return 1; }
else return 0;
}
template<typename T>
bool chmax(T& M1, T M2) {
if (M1 < M2) { M1 = M2; return 1; }
else return 0;
}
template<typename T>
auto vmax(T a) {
return *max_element(all(a));
}
template<typename T>
auto vmin(T a) {
return *min_element(all(a));
}
template<typename T>
auto vmaxi(T a) {
return max_element(all(a)) - a.begin();
}
template<typename T>
auto vmini(T a) {
return min_element(all(a)) - a.begin();
}
template<typename T>
auto vsum(vector<T> a) {
T x = 0;
for (auto i : a)x += i;
return x;
}
template<typename T>
vec<T> inv(vec<T> a) {//0-indexed 逆関数
vec<T> ans(a.sz);
rp(i, a.sz) {
ans[a[i]] = i;
}
return ans;
}
template<typename T>
vec<T> inv1(vec<T> a) {//1-indexed
vec<T> ans(a.sz);
rp(i, a.sz) {
ans[a[i] - 1] = i + 1;
}
return ans;
}
template<typename T>
vec<T> zat(vec<T> a) {//座標圧縮 T=ll,int
auto b = a;
sort(all(b));
b.erase(unique(all(b)), b.end());
vec<T> c(a.size());
rp(i, a.size()) {
c[i] = lwb(all(b), a[i]) - b.begin();
}
return c;
}
template<typename T>
vec<T> rsw(vec<T> a, bool is_put0 = 1) {//累積和 T=ll,int
if (is_put0 == 0) {
vec<T> b = {};
rp(i, a.sz) b.pb(a[i] + (b.sz == 0 ? 0 : b[b.sz - 1]));
return b;
}
vec<T> b = { 0 };
rp(i, a.sz) b.pb(a[i] + b[b.sz - 1]);
return b;
}
template<typename T>
T rswsum(vec<T>& a, int l, int r, bool is_put0 = 1) {//rsw配列から元の配列の[l,r)番目(0indexed)の和を取得
if (is_put0 == 0) {
assert(0 <= l && l <= r);
assert(r <= a.sz);
return (r == 0 ? 0 : a[r - 1]) - (l == 0 ? 0 : a[l - 1]);
}
assert(0 <= l && l <= r);
assert(r < a.sz);
return a[r] - a[l];
}
template<typename T>
T rswsum2(vec<T>& a, int l, int r, bool is_put0 = 1) {//rsw配列から元の配列の[l,r]番目(0indexed)の和を取得
return rswsum(a, l, r + 1, is_put0);
}
//文字列系
vector<pair<char, ll>> rle(string rr) {
vector<pair<char, ll>> ret;
char lc;
rep(i, 0, rr.size()) {
if (i > 0 && rr[i] == lc) ret[ret.sz - 1].second++;
else { ret.pb({ rr[i],1 }); }
lc = rr[i];
}
return ret;
}
vector<pair<int, ll>> rle(vi rr) {
vector<pair<int, ll>> ret;
int lc;
rep(i, 0, rr.size()) {
if (i > 0 && rr[i] == lc) ret[ret.sz - 1].second++;
else { ret.pb({ rr[i],1 }); }
lc = rr[i];
}
return ret;
}
vector<pair<ll, ll>> rle(vll rr) {
vector<pair<ll, ll>> ret;
ll lc;
rep(i, 0, rr.size()) {
if (i > 0 && rr[i] == lc) ret[ret.sz - 1].second++;
else { ret.pb({ rr[i],1 }); }
lc = rr[i];
}
return ret;
}
bool kai(string S) {//回文か判定
bool ans = 1;
rp(i, S.size()) if (S[i] != S[S.size() - 1 - i]) ans = 0;
return ans;
}
template <typename... Args>
string concat(const Args&... args) {//任意個のchat・string・int等を引数に取り文字列として繋げたstringを返す(整数はasciiでcharに変換)
string res;
(res += ... += args);
return res;
}
//その他
ll max(ll a, int b) { return max(a, ll(b)); }
ll max(int a, ll b) { return max(ll(a), b); }
ll min(ll a, int b) { return min(a, ll(b)); }
ll min(int a, ll b) { return min(ll(a), b); }
bool yn(bool jg) {
if (jg) {
cout << "Yes" << endl; return true;
}
else {
cout << "No" << endl; return false;
}
}
bool ynab(bool jg) {
if (jg) {
cout << "Alice" << endl; return true;
}
else {
cout << "Bob" << endl; return false;
}
}
template<typename T>
void cp(map < T, ll >& a, T b, ll c) {//countplus
if (a.find(b) == a.end()) a[b] = c;
else a[b] += c;
if (a[b] == 0) a.erase(b);
}
template<typename T>
bool cross(T a, T b, T c, T d) {//区間(a,b)と区間(c,d)が重なるか判定
return !(b <= c || d <= a);
}
template<typename T>
bool crosse(T a, T b, T c, T d) {//区間[a,b]と区間[c,d]が重なるか判定
return !(b < c || d < a);
}
template<typename T>
vec<vll> absort(vec<T> a, vec<T> b) {//l,rのl昇順r逆順sort
vec<vec<T>> ab(a.sz);
rp(i, a.sz) ab[i] = { a[i],-b[i],i };
sort(all(ab));
rp(i, a.sz) ab[i][1] = -ab[i][1];
return ab;
}
template<typename T>
bool rabc(T a, T b, T c) {//円環状でa,b,cがこの順か判定 同じ値はfalse
return ((a - b) / abs(a - b)) * ((b - c) / abs(b - c)) * ((c - a) / abs(c - a)) > 0;
}
bool labc(ll a, ll b, ll c) {//a<=b<cか判定
return a <= b && b < c;
}
#define inr labc
bool labc2(ll a, ll b, ll c) {//a<=b<=cか判定
return a <= b && b <= c;
}
#define inr2 labc2
vector<vector<char>> rot(vs a) {//時計回り90度回転
vector<vector<char>> r(a[0].sz, vector<char>(a.sz));
rp(i, a.sz)rp(j, a[0].sz) r[j][a[0].sz - 1 - i] = a[i][j];
return r;
}
template<typename T>
vector<vector<T>> rot(vector<vector<T>> a) {
vector<vector<T>> r(a[0].sz, vector<T>(a.sz));
rp(i, a.sz)rp(j, a[0].sz) r[j][a.sz - 1 - i] = a[i][j];
return r;
}
//実行時間調整付きassert
std::chrono::steady_clock::time_point START_TIME;
void start() {
START_TIME = std::chrono::steady_clock::now();
}
void assertt(bool b, int t) {
if (b) return;
if (START_TIME.time_since_epoch().count() == 0) {
start();
}
auto target_time = START_TIME + std::chrono::milliseconds(t - 100);
while (std::chrono::steady_clock::now() < target_time);
assert(0);
}
bool testt(int t) {//tミリ秒経っていないならtrue (while(testt(1950))のように使う)
assert(START_TIME.time_since_epoch().count() != 0);
auto target_time = START_TIME + std::chrono::milliseconds(t - 100);
return (std::chrono::steady_clock::now() < target_time);
}
//lazy_segtree<S, op, e, F, mapping, composition, id> seg(n);
//S:中身型 op:左右合成 e:初期値
//F:遅延型 mapping:遅延適用後の要素 composition:遅延合成( 関数f(g()) ) id:遅延初期値(何もさせない)
using S = ll;
using F = ll;
S op(S a, S b) {
return max(a, b);
}
S e() {
return -lmax;
}
using segt = segtree<S, op, e>;
/*
S mapping(F x, S a) {//xをaに作用(x初期値に注意) S[l]~S[r]のopであるSにF適用するとF(S[l])~F(S[r])のopになる必要がある 、つまりL~Rの代表にFかけてもL~Rの代表であり続けられるようS作る必要がある
if(x==0) return a;
else return {a.se,a.se};
}
F composition(F f, F g) {//fの方が後(f初期値に注意) Fを何個合成しても1つのFで表せる
if(f==0 && g==0 )return 0;
return 1;
}
F id() { return 0; }
using lsegt = lazy_segtree<S, op, e, F, mapping, composition, id>;
*/
//cout<<setprecision(15)<<fixed<<
//function<返り値の型(引数の型1, 引数の型2, ...)> 関数名 = [&](引数の型1 引数名1, 引数の型2, 引数名2, ...)
//function<ll(int,int)> f=[&](int a,int b)
//再帰しない場合 auto f=[&](int a,int b) ->ll{}
int mxkj;//階乗に入れる値の最大値
vector<mint> kj, gkj;
bool iskjset = 0;
void kjset(int maxkj) {
iskjset = 1;
mxkj = maxkj;
kj.resize(mxkj + 1);
gkj.resize(mxkj + 1);
kj[0] = 1;//階乗
rep(i, 1, mxkj + 1) {
kj[i] = kj[i - 1] * i;
}
gkj[mxkj] = 1 / kj[mxkj];
rrp(i, mxkj) gkj[i] = gkj[i + 1] * (i + 1);
}
auto cmb = [](int fst, int snd) {
assert(iskjset);
bool ck = 1;//範囲外値でエラーを返すなら1(ck=0でもpowの引数など他の値が範囲外にならないか要確認)
if (0 <= fst && fst <= mxkj && 0 <= snd && snd <= fst);
else {
if (ck) assert(0);
else return mint(0);
}
return kj[fst] * gkj[snd] * gkj[fst - snd];
};
auto pmt = [](int fst, int snd) {
assert(iskjset);
bool ck = 1;//範囲外値でエラーを返すなら1(ck=0でもpowの引数など他の値が範囲外にならないか要確認)
if (0 <= fst && fst <= mxkj && 0 <= snd && snd <= fst);
else {
if (ck) assert(0);
else return mint(0);
}
return kj[fst] * gkj[fst - snd];
};
vec<mint> conv_sp(vmint a, vmint sp, ll mxi = 200100) {//疎な場合のconv高速化 aの長さN,spの非0係数K個としてO(NK)
vec<pair<int, mint>> sps;
int spmxi = -1;
rp(i, sp.size()) {
if (sp[i] != 0) {
sps.pb({ i,sp[i] });
spmxi = i;
}
}
if (spmxi == -1) return { 0 };
vmint r(min(mxi, ll(a.sz) + spmxi), 0);
rp(i, a.sz) {
for (auto j : sps) {
if (i + j.fi < mxi)r[i + j.fi] += j.se * a[i];
}
}
return r;
}
vec<mint> div_sp(vmint f, vmint sp, ll mxi = 200100) {//f/spをmxiまで計算 ただしspのx^0項非0 spの非0係数K個としてO(mxiK)
assert(sp.sz > 0 && sp[0] != 0);
vec<pair<int, mint>> sps;
int spmxi = -1;
rp(i, sp.size()) {
if (sp[i] != 0) {
sps.pb({ i,sp[i] });
spmxi = i;
}
}
vec<mint> r(mxi, 0);
f.resize(mxi);
mint gsp0 = 1 / sp[0];
rp(i, mxi) {
r[i] = f[i] * gsp0;
for (auto j : sps) {
if (i + j.fi < mxi)f[i + j.fi] -= r[i] * j.se;
}
}
return r;
}
vec<mint> conv(vmint a, vmint b, ll mxi = 200100) {//a.sz+b.sz=nとしてO(nlogn) a.sz+b.sz>2^23=8.3e6を超えると畳み込み不可能
if (a.sz > mxi) a.resize(mxi);
if (b.sz > mxi) b.resize(mxi);
vmint r = convolution(a, b);
if (r.size() > mxi) r.resize(mxi);
return r;
}
mint convget(vmint a, vmint b, ll i) {//conv(a,b)[i]をO(a.sz+b.sz+i)で求める
if (i < 0) return 0;
mint r = 0;
rp(ii, i + 1) {
if (ii < a.sz && i - ii < b.sz)r += a[ii] * b[i - ii];
}
return r;
}
vec<mint> vinv(vmint f, ll mxi = 200100) {// O(mxi・logmxi)
assert(f.sz > 0 && f[0] != 0);
vec<mint> g = { mint(1) / f[0] };
f.resize(mxi); // fを最初にリサイズ
for (ll len = 1; len < mxi; len <<= 1) {//g←g(2-fg)をlog(mxi)回
int need = min(mxi, len << 1);
auto fg = conv(vec<mint>(f.begin(), f.begin() + need), g, need); // f * g
for (int i = 0; i < need; i++) fg[i] = -fg[i];
fg[0] += 2; // 2 - f*g
g = conv(g, fg, need);
}
return g;
}
vmint log(vmint f, ll mxi = 200100) {//log(f)を求める(ただしf[0]=1が必要) O(mxi・logmxi) ∫(f')/f
if (f.sz > mxi) f.resize(mxi);
assert(f[0] == 1);
if (f.sz == 1) return { 0 };
vmint bf(f.sz - 1);//fの微分
rp(i, f.sz - 1) bf[i] = f[i + 1] * (i + 1);
vmint bg = conv(bf, vinv(f, mxi), mxi);
vmint g(bg.sz);
g[0] = 0;
rp(i, bg.sz - 1) g[i + 1] = bg[i] / (i + 1);
return g;
}
vmint exp(vmint f, ll mxi = 200100) {//exp(f)をニュートン法で求める(ただしf[0]=0が必要) O(mxi・logmxi)
assert(f[0] == 0);
vec<mint> g = { 1 };
f.resize(mxi); // fを最初にリサイズ
for (ll len = 1; len < mxi; len <<= 1) {//g←g(1-log(g)+f)をlog(mxi)回
int need = min(mxi, len << 1);
vmint x = log(g, need);
x.resize(need);
rp(i, need) x[i] = f[i] - x[i];
x[0]++;
g = conv(g, x, need);
}
return g;
}
vec<mint> vpow(vmint a, ll p, ll mxi = 200100) {//a[0]+a[1]x+a[2]x^2...のp乗をa^p=exp(log(a))を利用して計算 O(mxi・logmxi)
int d = 0;//前から何個0が続くか
rp(i, a.sz) {
if (a[i] == 0) d++;
else break;
}
assert(p >= 0 || d == 0);//p<0かつd>0は計算不能(FPSで定義されない)
if (p == 0 || double(d) * p >= mxi || d == a.sz) {//0乗 or all zero
vmint r(mxi, 0);
if (p == 0) r[0] = 1;
return r;
}
//a[0]=1になるように前d個の0を消し、a全体をa[0]で割る補正
mint c = 1, ad = 1;
if (a[d] != 1) {
ad = a[d];
c = 1 / a[d];
rp(i, a.sz) a[i] *= c;
}
if (d > 0) {
rp(i, a.sz - d)a[i] = a[i + d];
a.resize(a.sz - d);
}
vmint ploga = log(a, mxi - d * p);//p*log(a)
rp(i, ploga.sz) ploga[i] *= p;
vmint r = exp(ploga, mxi - d * p);
mint adp;//ad^p
if (p < 0) adp = mint(c).pow(-p);
else adp = ad.pow(p);
rp(i, r.sz) r[i] *= adp;
r.resize(mxi);
rrp(i, mxi) {
if (i < d * p)r[i] = 0;
else r[i] = r[i - d * p];
}
return r;
}
vec<mint> vap(vvmint a, ll mxi = 200100) {//多項式総積 次数の総和NとしてO(N(logN)^2)
if (a.sz == 0) return { 1 };
queue<vmint> q;
for (auto& i : a) q.push(i);
while (q.sz > 1) {
vmint p1 = q.front();
q.pop();
vmint p2 = q.front();
q.pop();
vmint np = conv(p1, p2, mxi);
q.push(np);
}
return q.front();
}
vec<mint> vquot(vmint g, vmint f) {//多項式除算 N次g,M次fに対してg=qf+r(m-1次以下)を満たすqをO(NlogN)で求める
while (f.sz > 0 && f[f.sz - 1] == 0) f.pop_back();
assert(f.sz != 0);
while (g.sz > 0 && g[g.sz - 1] == 0) g.pop_back();
if (g.sz < f.sz) return {};
int n = int(g.sz) - 1, m = int(f.sz) - 1;
vmint revg = g; reverse(all(revg));
vmint revf = f; reverse(all(revf));
vmint revq = conv(revg, vinv(revf, n - m + 1), n - m + 1);
revq.resize(n - m + 1);
reverse(all(revq));//ここでrevqがqを表すようになる
return revq;
}
vec<mint> vmod(vmint g, vmint f) {//多項式の余り N次g,M次fに対してg=qf+r(m-1次以下)を満たすrをO(NlogN)で求める
while (f.sz > 0 && f[f.sz - 1] == 0) f.pop_back();
assert(f.sz != 0);
vmint q = vquot(g, f);
vmint qf = conv(q, f, f.sz - 1);
vmint r(f.sz - 1);
g.resize(f.sz - 1);
qf.resize(f.sz - 1);
rp(i, f.sz - 1) {
r[i] = g[i] - qf[i];
}
while (r.sz > 0 && r[r.sz - 1] == 0) r.pop_back();
return r;
}
vec<mint> vpowmod(vmint g, vmint f, ll p) {//多項式の余り g^p mod f f,gの次数NとしてO(NlogNlogp)
vmint r = { 1 };
assert(p < (ll(1) << 60));
rrp(i, 60) {
r = conv(r, r, 2 * r.sz);
r = vmod(r, f);
if (p & (ll(1) << i)) {
r = conv(r, g, r.sz + g.sz);
r = vmod(r, f);
}
}
return r;
}
vec<mint> vplus(vmint f, vmint g) {//f+g
if (f.sz > g.sz) swap(f, g);
vmint r(g.sz, 0);
rp(i, f.sz) r[i] = f[i] + g[i];
rep(i, f.sz, g.sz) r[i] = g[i];
return r;
}
mint vdn(vmint f, mint a) {//f(x)にaを代入(f(a)を計算)
mint r = 0;
rp(i, f.sz) r += f[i] * a.pow(i);
return r;
}
vec<mint> v1pow(ll p, ll mxi = 200100) {//(1/(1-x))={1,1,1,...}^pをmxiまでO(mxi)で求める p+mxiまでkjの前計算が必要 gkjが求まっていない場合はO(mxi・log998)
assert(p + mxi - 1 <= mxkj);
if (p == 0) {
vmint r(mxi, 0);
r[0] = 1;
return r;
}
vmint r(mxi);
rp(i, mxi) r[i] = cmb(p + i - 1, i);
return r;
}
vec<mint> v1apow(mint a, ll p, ll mxi = 200100) {//(1+ax)^pをmxiまでa==1でO(mxi),a!=1でO(mxi・logp)で求める mxiまでkjの前計算が必要 gkjが求まっていない場合はO(mxi・log998)
assert(mxi <= mxkj);
vmint r(mxi, 0);
ll siz = min(mxi, p + 1);
if (a == 1) rp(i, siz) {
r[i] = cmb(p, i);
}
else rp(i, siz) {
r[i] = cmb(p, i) * a.pow(i);
}
return r;
}
template<typename T>
mint parsum(vec<T> a, T s) {//部分和問題 配列aから0個以上選んで和をsにする通り数 aの総和xとしてO(x(logx)^2)
if (s < 0) return 0;
int n = a.sz;
vvmint p(n);
rp(i, n) {
p[i] = vmint(a[i] + 1, 0);
p[i][0] = 1;
p[i][a[i]] += 1;
}
vmint ans = vap(p, s + 1);
if (ans.sz <= s)return 0;
return ans[s];
}
vmint apowsum(vmint a, ll m) {//長さNの配列aに対しΣ(a[i]^k)をk=0,1,2...Mに対してO(N(logN)^2+MlogM)で列挙
int n = a.sz;
vvmint x(n);
rp(i, n) x[i] = { 1,-a[i] };
vmint y = vap(x, n + 1);
y = log(y, m + 1);
rp(i, y.sz) y[i] = -y[i] * i;
y[0] = n;
return y;
}
vec<mint> ktms(vmint d, ll n) {//a.sz=d.sz=kとして aの漸化式ai=d_0*a_(i-1)+...+d_(k-1)*a_(i-k)のときa_n=x0a0+...+x_(k-1)a_(k-1)を満たす配列xをO(KlogKlogN)
int k = d.sz;
reverse(all(d));
vmint q(k + 1);
rp(i, k) q[i] = -d[i];
q[k] = 1;
vmint r = vpowmod({ 0,1 }, q, n);
r.resize(k);
return r;
}
mint bm(vmint p, vmint q, ll n) {// bostan-mori [x^n] P(x)/Q(x)をP,Qの次数KとしてO(KlogKlogN)
if (p.sz != 0) p.pb(0);
if (n == 0) return p[0] / q[0];
vmint mq = q;
for (int i = 0; i < mq.sz; i += 2) mq[i] = -mq[i];
vmint u = conv(p, mq, p.sz + mq.sz), v2 = conv(q, mq, q.sz + mq.sz);
vmint v;
for (int i = 0; i < v2.sz; i += 2) v.pb(v2[i]);
if (n % 2 == 0) {
vmint ue;
for (int i = 0; i < u.sz; i += 2) ue.pb(u[i]);
return bm(ue, v, n / 2);
}
else {
vmint ue;
for (int i = 1; i < u.sz; i += 2) ue.pb(u[i]);
return bm(ue, v, n / 2);
}
}
mint tobm(vmint a, vmint d, ll n) {//a.sz=d.sz=kとして aの漸化式ai=d_0*a_(i-1)+...+d_(k-1)*a_(i-k)のときa_n=x0a0+...+x_(k-1)a_(k-1)をO(KlogKlogN)
assert(a.sz == d.sz);
ll k = a.sz;
vmint q = { 1 };
for (auto i : d) q.pb(-i);
vmint p = conv(a, q, k);
return bm(p, q, n);
}
//Berlekamp–Massey aの漸化式ai=d_0*a_(i-1)+...+d_(k-1)*a_(i-k)のとき配列{1,-d_0,-d_1,...}をa.sz=NとしてO(N^2)
//L=q.sz(q:返り値)としてN<2*Lなら解は複数存在 2*L<=Nなら解は唯一
//qに対して末尾の0を削除してはならない
vmint bm2(vmint a) {
vmint q = { 1 },b=q;
int l = 0, pn = -1;
mint pd = 1;
rp(n, a.sz) {
mint d = 0;
rp(j, n + 1) if(j<q.sz && n-j<a.sz)d += q[j] * a[n - j];
if (d == 0) continue;
vmint qnew = q;
mint k = d / pd;
if (qnew.sz < b.sz + n - pn) qnew.resize(b.sz + n - pn);
rp(j, b.sz) {
qnew[j + n - pn] -= k * b[j];
}
if (2 * l <= n) {
l = n + 1 - l;
b = q;
q = qnew;
pn = n;
pd = d;
}
else {
q = qnew;
}
}
return q;
}
//線形漸化式を持つ数列aのk番目の値を予測
//返り値のfi=falseなら一意に定まらない(aが短すぎて複数解を持つ),trueなら一意に定まる
pair<bool,mint> bmbm(vmint a,ll k){
pair<bool, mint> r;
vmint q = bm2(a);
if (q.sz * 2 <= a.sz) r.fi = true;
else r.fi = false;
r.se = bm(conv(a, q, q.sz), q, k);
return r;
}
int main() {
ll a, b, c, d, e, n;
cin >> a >> b >> c >> d >> e >> n;
vmint f(10);
f[0] = a;
f[1] = b;
rep(i, 2, 10) f[i] = c * f[i - 1] + d * f[i - 2] + e;
f = rsw(f, 0);
auto ans = bmbm(f, n);
cout << ans.se << endl;
}