結果
| 問題 | No.2524 Stripes |
| ユーザー |
 ttttan2
|
| 提出日時 | 2023-11-01 00:24:03 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 1,808 ms / 7,000 ms |
| コード長 | 64,523 bytes |
| コンパイル時間 | 4,118 ms |
| コンパイル使用メモリ | 246,004 KB |
| 実行使用メモリ | 28,256 KB |
| 最終ジャッジ日時 | 2024-09-25 17:47:56 |
| 合計ジャッジ時間 | 14,705 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge5 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
5,248 KB |
| testcase_01 | AC | 1 ms
5,248 KB |
| testcase_02 | AC | 2 ms
5,376 KB |
| testcase_03 | AC | 604 ms
17,536 KB |
| testcase_04 | AC | 20 ms
5,376 KB |
| testcase_05 | AC | 331 ms
11,264 KB |
| testcase_06 | AC | 600 ms
17,396 KB |
| testcase_07 | AC | 896 ms
24,044 KB |
| testcase_08 | AC | 1,060 ms
24,188 KB |
| testcase_09 | AC | 149 ms
7,936 KB |
| testcase_10 | AC | 473 ms
15,232 KB |
| testcase_11 | AC | 14 ms
5,376 KB |
| testcase_12 | AC | 122 ms
7,040 KB |
| testcase_13 | AC | 1,029 ms
26,240 KB |
| testcase_14 | AC | 1,212 ms
27,272 KB |
| testcase_15 | AC | 1,144 ms
26,240 KB |
| testcase_16 | AC | 1,808 ms
28,256 KB |
| testcase_17 | AC | 189 ms
26,096 KB |
| testcase_18 | AC | 2 ms
5,376 KB |
| testcase_19 | AC | 2 ms
5,376 KB |
| testcase_20 | AC | 1 ms
5,376 KB |
| testcase_21 | AC | 1 ms
5,376 KB |
| testcase_22 | AC | 2 ms
5,376 KB |
| testcase_23 | AC | 2 ms
5,376 KB |
| testcase_24 | AC | 1 ms
5,376 KB |
| testcase_25 | AC | 2 ms
5,376 KB |
| testcase_26 | AC | 2 ms
5,376 KB |
| testcase_27 | AC | 2 ms
5,376 KB |
ソースコード
#include <algorithm>
#include <bitset>
#include <complex>
#include <cstring>
#include <deque>
#include <exception>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iosfwd>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <locale>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <stdexcept>
#include <streambuf>
#include <string>
#include <typeinfo>
#include <utility>
#include <valarray>
#include <vector>
#if __cplusplus >= 201103L
#include <array>
#include <atomic>
#include <chrono>
#include <condition_variable>
#include <forward_list>
#include <future>
#include <initializer_list>
#include <mutex>
#include <random>
#include <ratio>
#include <regex>
#include <scoped_allocator>
#include <system_error>
#include <thread>
#include <tuple>
#include <typeindex>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#endif
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef unsigned int ui;
typedef pair<int,int> pii;
typedef pair<pii,int> ppii;
typedef pair<int,pii> pipi;
typedef pair<ll,ll> pll;
typedef pair<pll,ll> ppll;
typedef pair<ll,pll> plpl;
typedef pair<pii,pii> pippi;
typedef tuple<ll,ll,ll> tl;
typedef pair<long double,long double> pdd;
//typedef vector<vector<ll>> mat;
const ll mod=1000000007;
const ll mod2=998244353;
const ll mod3=1000000009;
ll inf=numeric_limits<ll>::max()/2-1;
int iinf=numeric_limits<int>::max()/2-1;
double pi=3.14159265358979323846;
double eps=1e-8;
#define rep(i,m,n) for(ll i=m;i<n;i++)
#define rrep(i,n,m) for(ll i=n;i>=m;i--)
#define srep(itr,st) for(auto itr=st.begin();itr!=st.end();itr++)
#define mrep(itr,mp) for(auto& itr:mp)
#define Max(a,b) a=max(a,b)
#define Min(a,b) a=min(a,b)
int dh[4]={1,0,-1,0};
int dw[4]={0,1,0,-1};
int ddh[8]={-1,-1,-1,0,0,1,1,1};
int ddw[8]={-1,0,1,-1,1,-1,0,1};
struct custom_hash {
static uint64_t splitmix64(uint64_t x) {
x+=0x9e3779b97f4a7c15;x=(x^(x>>30))*0xbf58476d1ce4e5b9;x=(x^(x>>27))*0x94d049bb133111eb;
return x^(x>>31);}
size_t operator()(uint64_t x) const {
static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
return splitmix64(x + FIXED_RANDOM);}
};
#define umh unordered_map<int,ll,custom_hash>
ll gcd(ll a,ll b){
if(a<0)a=-a;if(b<0)b=-b;if(a<b)swap(a,b);if(b==0)return a;if(a%b==0)return b;return gcd(b,a%b);}
ll lcm(ll a,ll b){if(a==0)return b;if(b==0)return a;ll c=gcd(a,b);a/=c;a*=b;return a;}
ll Pow(ll n,ll k){
if(k<0)return 0;ll ret=1;ll now=n;while(k>0){if(k&1)ret*=now;now*=now;k/=2;}return ret;
}
ll beki(ll n,ll k,ll md){
ll ret=1;ll now=n;now%=md;
while(k>0){
if(k%2==1){ret*=now;ret%=md;}
now*=now;now%=md;k=k>>1;}return ret;
}
ll gyaku(ll n,ll md){return beki(n,md-2,md);}
ll popcount(ll n){ll ret=0;ll u=n;while(u>0){ret+=u%2;u/=2;}return ret;}
#ifndef ATCODER_INTERNAL_BITOP_HPP
#define ATCODER_INTERNAL_BITOP_HPP 1
#ifdef _MSC_VER
#include <intrin.h>
#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;
for (long long a : {2, 7, 61}) {
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;
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);
unsigned long long floor_sum_unsigned(unsigned long long n,
unsigned long long m,
unsigned long long a,
unsigned long long b) {
unsigned long long ans = 0;
while (true) {
if (a >= m) {
ans += n * (n - 1) / 2 * (a / m);
a %= m;
}
if (b >= m) {
ans += n * (b / m);
b %= m;
}
unsigned long long y_max = a * n + b;
if (y_max < m) break;
// y_max < m * (n + 1)
// floor(y_max / m) <= n
n = (unsigned long long)(y_max / m);
b = (unsigned long long)(y_max % m);
std::swap(m, a);
}
return ans;
}
}
}
#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--) {
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--) {
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;
}
}
void change(int p,T x){
add(p,x-data[p]);
}
T sum(int l, int r) {
assert(0 <= l && l <= r && r <= _n);
return sum(r) - sum(l);
}
int lb(T w){
if(w<=0)return 0;
int x=0;
int u=1;while(u<_n)u*=2;
for(int k=u;k>0;k/=2){
if(x+k<=_n&&data[x+k-1]<w){
w-=data[x+k-1];
x+=k;
}
}
return x;
}
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_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_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
using namespace atcoder;
#define endl "\n"
//using mint=static_modint<mod2>;
template<int MOD> struct Fp {
// inner value
long long val;
// constructor
constexpr Fp() : val(0) { }
constexpr Fp(long long v) : val(v % MOD) {
if (val < 0) val += MOD;
}
constexpr long long get() const { return val; }
constexpr int get_mod() const { return MOD; }
// arithmetic operators
constexpr Fp operator + () const { return Fp(*this); }
constexpr Fp operator - () const { return Fp(0) - Fp(*this); }
constexpr Fp operator + (const Fp &r) const { return Fp(*this) += r; }
constexpr Fp operator - (const Fp &r) const { return Fp(*this) -= r; }
constexpr Fp operator * (const Fp &r) const { return Fp(*this) *= r; }
constexpr Fp operator / (const Fp &r) const { return Fp(*this) /= r; }
constexpr Fp& operator += (const Fp &r) {
val += r.val;
if (val >= MOD) val -= MOD;
return *this;
}
constexpr Fp& operator -= (const Fp &r) {
val -= r.val;
if (val < 0) val += MOD;
return *this;
}
constexpr Fp& operator *= (const Fp &r) {
val = val * r.val % MOD;
return *this;
}
constexpr Fp& operator /= (const Fp &r) {
long long a = r.val, b = MOD, u = 1, v = 0;
while (b) {
long long t = a / b;
a -= t * b, swap(a, b);
u -= t * v, swap(u, v);
}
val = val * u % MOD;
if (val < 0) val += MOD;
return *this;
}
constexpr Fp pow(long long n) const {
Fp res(1), mul(*this);
while (n > 0) {
if (n & 1) res *= mul;
mul *= mul;
n >>= 1;
}
return res;
}
constexpr Fp inv() const {
Fp res(1), div(*this);
return res / div;
}
// other operators
constexpr bool operator == (const Fp &r) const {
return this->val == r.val;
}
constexpr bool operator != (const Fp &r) const {
return this->val != r.val;
}
constexpr Fp& operator ++ () {
++val;
if (val >= MOD) val -= MOD;
return *this;
}
constexpr Fp& operator -- () {
if (val == 0) val += MOD;
--val;
return *this;
}
constexpr Fp operator ++ (int) const {
Fp res = *this;
++*this;
return res;
}
constexpr Fp operator -- (int) const {
Fp res = *this;
--*this;
return res;
}
friend constexpr istream& operator >> (istream &is, Fp<MOD> &x) {
is >> x.val;
x.val %= MOD;
if (x.val < 0) x.val += MOD;
return is;
}
friend constexpr ostream& operator << (ostream &os, const Fp<MOD> &x) {
return os << x.val;
}
friend constexpr Fp<MOD> pow(const Fp<MOD> &r, long long n) {
return r.pow(n);
}
friend constexpr Fp<MOD> inv(const Fp<MOD> &r) {
return r.inv();
}
};
namespace NTT {
long long modpow(long long a, long long n, int mod) {
long long res = 1;
while (n > 0) {
if (n & 1) res = res * a % mod;
a = a * a % mod;
n >>= 1;
}
return res;
}
long long modinv(long long a, int mod) {
long long b = mod, u = 1, v = 0;
while (b) {
long long t = a / b;
a -= t * b, swap(a, b);
u -= t * v, swap(u, v);
}
u %= mod;
if (u < 0) u += mod;
return u;
}
int calc_primitive_root(int mod) {
if (mod == 2) return 1;
if (mod == 167772161) return 3;
if (mod == 469762049) return 3;
if (mod == 754974721) return 11;
if (mod == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
long long x = (mod - 1) / 2;
while (x % 2 == 0) x /= 2;
for (long long i = 3; 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 (modpow(g, (mod - 1) / divs[i], mod) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
int get_fft_size(int N, int M) {
int size_a = 1, size_b = 1;
while (size_a < N) size_a <<= 1;
while (size_b < M) size_b <<= 1;
return max(size_a, size_b) << 1;
}
// number-theoretic transform
template<class mint> void trans(vector<mint> &v, bool inv = false) {
if (v.empty()) return;
int N = (int)v.size();
int MOD = v[0].get_mod();
int PR = calc_primitive_root(MOD);
static bool first = true;
static vector<long long> vbw(30), vibw(30);
if (first) {
first = false;
for (int k = 0; k < 30; ++k) {
vbw[k] = modpow(PR, (MOD - 1) >> (k + 1), MOD);
vibw[k] = modinv(vbw[k], MOD);
}
}
for (int i = 0, j = 1; j < N - 1; j++) {
for (int k = N >> 1; k > (i ^= k); k >>= 1);
if (i > j) swap(v[i], v[j]);
}
for (int k = 0, t = 2; t <= N; ++k, t <<= 1) {
long long bw = vbw[k];
if (inv) bw = vibw[k];
for (int i = 0; i < N; i += t) {
mint w = 1;
for (int j = 0; j < t/2; ++j) {
int j1 = i + j, j2 = i + j + t/2;
mint c1 = v[j1], c2 = v[j2] * w;
v[j1] = c1 + c2;
v[j2] = c1 - c2;
w *= bw;
}
}
}
if (inv) {
long long invN = modinv(N, MOD);
for (int i = 0; i < N; ++i) v[i] = v[i] * invN;
}
}
// for garner
static constexpr int MOD0 = 754974721;
static constexpr int MOD1 = 167772161;
static constexpr int MOD2 = 469762049;
using mint0 = Fp<MOD0>;
using mint1 = Fp<MOD1>;
using mint2 = Fp<MOD2>;
static const mint1 imod0 = 95869806; // modinv(MOD0, MOD1);
static const mint2 imod1 = 104391568; // modinv(MOD1, MOD2);
static const mint2 imod01 = 187290749; // imod1 / MOD0;
// small case (T = mint, long long)
template<class T> vector<T> naive_mul(const vector<T> &A, const vector<T> &B) {
if (A.empty() || B.empty()) return {};
int N = (int)A.size(), M = (int)B.size();
vector<T> res(N + M - 1);
for (int i = 0; i < N; ++i)
for (int j = 0; j < M; ++j)
res[i + j] += A[i] * B[j];
return res;
}
// mul by convolution
template<class mint> vector<mint> mul(const vector<mint> &A, const vector<mint> &B) {
if (A.empty() || B.empty()) return {};
int N = (int)A.size(), M = (int)B.size();
if (min(N, M) < 30) return naive_mul(A, B);
int MOD = A[0].get_mod();
int size_fft = get_fft_size(N, M);
if (MOD == 998244353) {
vector<mint> a(size_fft), b(size_fft), c(size_fft);
for (int i = 0; i < N; ++i) a[i] = A[i];
for (int i = 0; i < M; ++i) b[i] = B[i];
trans(a), trans(b);
vector<mint> res(size_fft);
for (int i = 0; i < size_fft; ++i) res[i] = a[i] * b[i];
trans(res, true);
res.resize(N + M - 1);
return res;
}
vector<mint0> a0(size_fft, 0), b0(size_fft, 0), c0(size_fft, 0);
vector<mint1> a1(size_fft, 0), b1(size_fft, 0), c1(size_fft, 0);
vector<mint2> a2(size_fft, 0), b2(size_fft, 0), c2(size_fft, 0);
for (int i = 0; i < N; ++i)
a0[i] = A[i].val, a1[i] = A[i].val, a2[i] = A[i].val;
for (int i = 0; i < M; ++i)
b0[i] = B[i].val, b1[i] = B[i].val, b2[i] = B[i].val;
trans(a0), trans(a1), trans(a2), trans(b0), trans(b1), trans(b2);
for (int i = 0; i < size_fft; ++i) {
c0[i] = a0[i] * b0[i];
c1[i] = a1[i] * b1[i];
c2[i] = a2[i] * b2[i];
}
trans(c0, true), trans(c1, true), trans(c2, true);
mint mod0 = MOD0, mod01 = mod0 * MOD1;
vector<mint> res(N + M - 1);
for (int i = 0; i < N + M - 1; ++i) {
int y0 = c0[i].val;
int y1 = (imod0 * (c1[i] - y0)).val;
int y2 = (imod01 * (c2[i] - y0) - imod1 * y1).val;
res[i] = mod01 * y2 + mod0 * y1 + y0;
}
return res;
}
};
// Formal Power Series
template<typename mint> struct FPS : vector<mint> {
using vector<mint>::vector;
// constructor
constexpr FPS(const vector<mint> &r) : vector<mint>(r) {}
// core operator
constexpr FPS pre(int siz) const {
return FPS(begin(*this), begin(*this) + min((int)this->size(), siz));
}
constexpr FPS rev() const {
FPS res = *this;
reverse(begin(res), end(res));
return res;
}
constexpr FPS& normalize() {
while (!this->empty() && this->back() == 0) this->pop_back();
return *this;
}
// basic operator
constexpr FPS operator - () const noexcept {
FPS res = (*this);
for (int i = 0; i < (int)res.size(); ++i) res[i] = -res[i];
return res;
}
constexpr FPS operator + (const mint &v) const { return FPS(*this) += v; }
constexpr FPS operator + (const FPS &r) const { return FPS(*this) += r; }
constexpr FPS operator - (const mint &v) const { return FPS(*this) -= v; }
constexpr FPS operator - (const FPS &r) const { return FPS(*this) -= r; }
constexpr FPS operator * (const mint &v) const { return FPS(*this) *= v; }
constexpr FPS operator * (const FPS &r) const { return FPS(*this) *= r; }
constexpr FPS operator / (const mint &v) const { return FPS(*this) /= v; }
constexpr FPS operator / (const FPS &r) const { return FPS(*this) /= r; }
constexpr FPS operator % (const FPS &r) const { return FPS(*this) %= r; }
constexpr FPS operator << (int x) const { return FPS(*this) <<= x; }
constexpr FPS operator >> (int x) const { return FPS(*this) >>= x; }
constexpr FPS& operator += (const mint &v) {
if (this->empty()) this->resize(1);
(*this)[0] += v;
return *this;
}
constexpr FPS& operator += (const FPS &r) {
if (r.size() > this->size()) this->resize(r.size());
for (int i = 0; i < (int)r.size(); ++i) (*this)[i] += r[i];
return this->normalize();
}
constexpr FPS& operator -= (const mint &v) {
if (this->empty()) this->resize(1);
(*this)[0] -= v;
return *this;
}
constexpr FPS& operator -= (const FPS &r) {
if (r.size() > this->size()) this->resize(r.size());
for (int i = 0; i < (int)r.size(); ++i) (*this)[i] -= r[i];
return this->normalize();
}
constexpr FPS& operator *= (const mint &v) {
for (int i = 0; i < (int)this->size(); ++i) (*this)[i] *= v;
return *this;
}
constexpr FPS& operator *= (const FPS &r) {
return *this = NTT::mul((*this), r);
}
constexpr FPS& operator /= (const mint &v) {
assert(v != 0);
mint iv = v.inv();
for (int i = 0; i < (int)this->size(); ++i) (*this)[i] *= iv;
return *this;
}
// division, r must be normalized (r.back() must not be 0)
constexpr FPS& operator /= (const FPS &r) {
assert(!r.empty());
assert(r.back() != 0);
this->normalize();
if (this->size() < r.size()) {
this->clear();
return *this;
}
int need = (int)this->size() - (int)r.size() + 1;
*this = (rev().pre(need) * r.rev().inv(need)).pre(need).rev();
return *this;
}
constexpr FPS& operator %= (const FPS &r) {
assert(!r.empty());
assert(r.back() != 0);
this->normalize();
FPS q = (*this) / r;
return *this -= q * r;
}
constexpr FPS& operator <<= (int x) {
FPS res(x, 0);
res.insert(res.end(), begin(*this), end(*this));
return *this = res;
}
constexpr FPS& operator >>= (int x) {
FPS res;
res.insert(res.end(), begin(*this) + x, end(*this));
return *this = res;
}
constexpr mint eval(const mint &v) {
mint res = 0;
for (int i = (int)this->size()-1; i >= 0; --i) {
res *= v;
res += (*this)[i];
}
return res;
}
// advanced operation
// df/dx
constexpr FPS diff() const {
int n = (int)this->size();
FPS res(n-1);
for (int i = 1; i < n; ++i) res[i-1] = (*this)[i] * i;
return res;
}
// \int f dx
constexpr FPS integral() const {
int n = (int)this->size();
FPS res(n+1, 0);
for (int i = 0; i < n; ++i) res[i+1] = (*this)[i] / (i+1);
return res;
}
// inv(f), f[0] must not be 0
constexpr FPS inv(int deg) const {
assert((*this)[0] != 0);
if (deg < 0) deg = (int)this->size();
FPS res({mint(1) / (*this)[0]});
for (int i = 1; i < deg; i <<= 1) {
res = (res + res - res * res * pre(i << 1)).pre(i << 1);
}
res.resize(deg);
return res;
}
constexpr FPS inv() const {
return inv((int)this->size());
}
// log(f) = \int f'/f dx, f[0] must be 1
constexpr FPS log(int deg) const {
assert((*this)[0] == 1);
FPS res = (diff() * inv(deg)).integral();
res.resize(deg);
return res;
}
constexpr FPS log() const {
return log((int)this->size());
}
// exp(f), f[0] must be 0
constexpr FPS exp(int deg) const {
assert((*this)[0] == 0);
FPS res(1, 1);
for (int i = 1; i < deg; i <<= 1) {
res = res * (pre(i << 1) - res.log(i << 1) + 1).pre(i << 1);
}
res.resize(deg);
return res;
}
constexpr FPS exp() const {
return exp((int)this->size());
}
// pow(f) = exp(e * log f)
constexpr FPS pow(long long e, int deg) const {
if (e == 0) {
FPS res(deg, 0);
res[0] = 1;
return res;
}
long long i = 0;
while (i < (int)this->size() && (*this)[i] == 0) ++i;
if (i == (int)this->size() || i > (deg - 1) / e) return FPS(deg, 0);
mint k = (*this)[i];
FPS res = ((((*this) >> i) / k).log(deg) * e).exp(deg) * mint(k).pow(e) << (e * i);
res.resize(deg);
return res;
}
constexpr FPS pow(long long e) const {
return pow(e, (int)this->size());
}
// sqrt(f), f[0] must be 1
constexpr FPS sqrt(int deg) const {
if((*this).size()==0)return FPS(deg,0);
if((*this)[0]==mint(0)){
for (int i = 1; i < (*this).size(); i++) {
if ((*this)[i] != mint(0)) {
if (i & 1) return {};
if (deg - i / 2 <= 0) break;
auto ret = ((*this) >> i).sqrt(deg - i/2);
if (ret.empty()) return {};
ret = ret << (i / 2);
if (ret.size() < deg) ret.resize(deg, mint(0));
return ret;
}
}
return FPS(deg, 0);
}
mint inv2 = mint(1) / mint(2);
FPS res(1, 1);
for (int i = 1; i < deg; i <<= 1) {
res = (res + pre(i << 1) * res.inv(i << 1))*inv2;
}
return res.pre(deg);
}
constexpr FPS sqrt() const {
return sqrt((int)this->size());
}
// friend operators
friend constexpr FPS diff(const FPS &f) { return f.diff(); }
friend constexpr FPS integral(const FPS &f) { return f.integral(); }
friend constexpr FPS inv(const FPS &f, int deg) { return f.inv(deg); }
friend constexpr FPS inv(const FPS &f) { return f.inv((int)f.size()); }
friend constexpr FPS log(const FPS &f, int deg) { return f.log(deg); }
friend constexpr FPS log(const FPS &f) { return f.log((int)f.size()); }
friend constexpr FPS exp(const FPS &f, int deg) { return f.exp(deg); }
friend constexpr FPS exp(const FPS &f) { return f.exp((int)f.size()); }
friend constexpr FPS pow(const FPS &f, long long e, int deg) { return f.pow(e, deg); }
friend constexpr FPS pow(const FPS &f, long long e) { return f.pow(e, (int)f.size()); }
friend constexpr FPS sqrt(const FPS &f, int deg) { return f.sqrt(deg); }
friend constexpr FPS sqrt(const FPS &f) { return f.sqrt((int)f.size()); }
};
/*/////////////////////////////*/
// Polynomial, FPS algorithms
/*/////////////////////////////*/
// Bostan-Mori
// find [x^N] P(x)/Q(x), O(K log K log N)
// deg(Q(x)) = K, deg(P(x)) < K
template<typename mint> mint BostanMori(const FPS<mint> &P, const FPS<mint> &Q, long long N) {
assert(!P.empty() && !Q.empty());
if (N == 0 || Q.size() == 1) return P[0] / Q[0];
int qdeg = (int)Q.size();
FPS<mint> P2{P}, minusQ{Q};
P2.resize(qdeg - 1);
for (int i = 1; i < (int)Q.size(); i += 2) minusQ[i] = -minusQ[i];
P2 *= minusQ;
FPS<mint> Q2 = Q * minusQ;
FPS<mint> S(qdeg - 1), T(qdeg);
for (int i = 0; i < (int)S.size(); ++i) {
S[i] = (N % 2 == 0 ? P2[i * 2] : P2[i * 2 + 1]);
}
for (int i = 0; i < (int)T.size(); ++i) {
T[i] = Q2[i * 2];
}
return BostanMori(S, T, N >> 1);
}
using mint = Fp<mod2>;
array<FPS<mint>,4> f(array<FPS<mint>,4> l,array<FPS<mint>,4> r){
array<FPS<mint>,4> ret;
rep(i,0,4){
int n1=((i>>1)&1)*2;
int n2=i%2;
ret[i]=l[n1]*r[n2]+l[n1+1]*r[n2+2];
}
return ret;
}
int main(){
ios::sync_with_stdio(false);cin.tie(nullptr);
int n;cin>>n;
string s;cin>>s;
queue<array<FPS<mint>,4>> q,q2;
vector<mint> v1={1},v2={0,1},v3={0},v4={1};
array<FPS<mint>,4> fr={FPS<mint>(v1),FPS<mint>(v2),FPS<mint>(v3),FPS<mint>(v4)};
array<FPS<mint>,4> fb={FPS<mint>(v1),FPS<mint>(v3),FPS<mint>(v2),FPS<mint>(v4)};
rrep(i,n-1,0){
if(s[i]=='R'){
q.push(fr);
}
else{
q.push(fb);
}
}
while(q.size()>1){
while(q2.size()>0)q2.pop();
while(q.size()>0){
array<FPS<mint>,4> f1=q.front();q.pop();
if(q.size()==0){
q2.push(f1);
break;
}
array<FPS<mint>,4> f2=q.front();q.pop();
q2.push(f(f1,f2));
}
swap(q,q2);
}
array<FPS<mint>,4> v=q.front();
rep(i,1,n+1){
mint ans=0;
rep(j,0,4){
if(v[j].size()>i){
ans+=v[j][i];
}
}
cout<<ans<<endl;
}
}