結果
| 問題 |
No.303 割れません
|
| ユーザー |
 NyaanNyaan
|
| 提出日時 | 2022-11-05 03:45:27 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 302 ms / 10,000 ms |
| コード長 | 60,082 bytes |
| コンパイル時間 | 5,642 ms |
| コンパイル使用メモリ | 328,868 KB |
| 最終ジャッジ日時 | 2025-02-08 18:31:08 |
|
ジャッジサーバーID （参考情報） |
judge5 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 14 |
ソースコード
/**
* date : 2022-11-05 03:45:17
*/
#define NDEBUG
using namespace std;
// intrinstic
#include <immintrin.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
// utility
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;
template <typename T, typename U>
struct P : pair<T, U> {
template <typename... Args>
P(Args... args) : pair<T, U>(args...) {}
using pair<T, U>::first;
using pair<T, U>::second;
P &operator+=(const P &r) {
first += r.first;
second += r.second;
return *this;
}
P &operator-=(const P &r) {
first -= r.first;
second -= r.second;
return *this;
}
P &operator*=(const P &r) {
first *= r.first;
second *= r.second;
return *this;
}
template <typename S>
P &operator*=(const S &r) {
first *= r, second *= r;
return *this;
}
P operator+(const P &r) const { return P(*this) += r; }
P operator-(const P &r) const { return P(*this) -= r; }
P operator*(const P &r) const { return P(*this) *= r; }
template <typename S>
P operator*(const S &r) const {
return P(*this) *= r;
}
P operator-() const { return P{-first, -second}; }
};
using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;
constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;
template <typename T>
int sz(const T &t) {
return t.size();
}
template <typename T, typename U>
inline bool amin(T &x, U y) {
return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
return (x < y) ? (x = y, true) : false;
}
template <typename T>
inline T Max(const vector<T> &v) {
return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
return accumulate(begin(v), end(v), 0LL);
}
template <typename T>
int lb(const vector<T> &v, const T &a) {
return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
return upper_bound(begin(v), end(v), a) - begin(v);
}
constexpr long long TEN(int n) {
long long ret = 1, x = 10;
for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
return ret;
}
template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
return make_pair(t, u);
}
template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
vector<T> ret(v.size() + 1);
if (rev) {
for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
} else {
for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
}
return ret;
};
template <typename T>
vector<T> mkuni(const vector<T> &v) {
vector<T> ret(v);
sort(ret.begin(), ret.end());
ret.erase(unique(ret.begin(), ret.end()), ret.end());
return ret;
}
template <typename F>
vector<int> mkord(int N,F f) {
vector<int> ord(N);
iota(begin(ord), end(ord), 0);
sort(begin(ord), end(ord), f);
return ord;
}
template <typename T>
vector<int> mkinv(vector<T> &v) {
int max_val = *max_element(begin(v), end(v));
vector<int> inv(max_val + 1, -1);
for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
return inv;
}
vector<int> mkiota(int n) {
vector<int> ret(n);
iota(begin(ret), end(ret), 0);
return ret;
}
template <typename T>
T mkrev(const T &v) {
T w{v};
reverse(begin(w), end(w));
return w;
}
template <typename T>
bool nxp(vector<T> &v) {
return next_permutation(begin(v), end(v));
}
template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;
} // namespace Nyaan
// bit operation
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
return _mm_popcnt_u64(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
} // namespace Nyaan
// inout
namespace Nyaan {
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
os << p.first << " " << p.second;
return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
is >> p.first >> p.second;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
int s = (int)v.size();
for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
for (auto &x : v) is >> x;
return is;
}
istream &operator>>(istream &is, __int128_t &x) {
string S;
is >> S;
x = 0;
int flag = 0;
for (auto &c : S) {
if (c == '-') {
flag = true;
continue;
}
x *= 10;
x += c - '0';
}
if (flag) x = -x;
return is;
}
istream &operator>>(istream &is, __uint128_t &x) {
string S;
is >> S;
x = 0;
for (auto &c : S) {
x *= 10;
x += c - '0';
}
return is;
}
ostream &operator<<(ostream &os, __int128_t x) {
if (x == 0) return os << 0;
if (x < 0) os << '-', x = -x;
string S;
while (x) S.push_back('0' + x % 10), x /= 10;
reverse(begin(S), end(S));
return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
if (x == 0) return os << 0;
string S;
while (x) S.push_back('0' + x % 10), x /= 10;
reverse(begin(S), end(S));
return os << S;
}
void in() {}
template <typename T, class... U>
void in(T &t, U &...u) {
cin >> t;
in(u...);
}
void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
cout << t;
if (sizeof...(u)) cout << sep;
out(u...);
}
void outr() {}
template <typename T, class... U, char sep = ' '>
void outr(const T &t, const U &...u) {
cout << t;
outr(u...);
}
struct IoSetupNya {
IoSetupNya() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(15);
cerr << fixed << setprecision(7);
}
} iosetupnya;
} // namespace Nyaan
// debug
#ifdef NyaanDebug
#define trc(...) (void(0))
#else
#define trc(...) (void(0))
#endif
// macro
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...) \
int __VA_ARGS__; \
in(__VA_ARGS__)
#define inl(...) \
long long __VA_ARGS__; \
in(__VA_ARGS__)
#define ins(...) \
string __VA_ARGS__; \
in(__VA_ARGS__)
#define in2(s, t) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i]); \
}
#define in3(s, t, u) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i]); \
}
#define in4(s, t, u, v) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i], v[i]); \
}
#define die(...) \
do { \
Nyaan::out(__VA_ARGS__); \
return; \
} while (0)
namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }
//
using namespace std;
template <uint32_t mod>
struct LazyMontgomeryModInt {
using mint = LazyMontgomeryModInt;
using i32 = int32_t;
using u32 = uint32_t;
using u64 = uint64_t;
static constexpr u32 get_r() {
u32 ret = mod;
for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
return ret;
}
static constexpr u32 r = get_r();
static constexpr u32 n2 = -u64(mod) % mod;
static_assert(r * mod == 1, "invalid, r * mod != 1");
static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");
u32 a;
constexpr LazyMontgomeryModInt() : a(0) {}
constexpr LazyMontgomeryModInt(const int64_t &b)
: a(reduce(u64(b % mod + mod) * n2)){};
static constexpr u32 reduce(const u64 &b) {
return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
}
constexpr mint &operator+=(const mint &b) {
if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
return *this;
}
constexpr mint &operator-=(const mint &b) {
if (i32(a -= b.a) < 0) a += 2 * mod;
return *this;
}
constexpr mint &operator*=(const mint &b) {
a = reduce(u64(a) * b.a);
return *this;
}
constexpr mint &operator/=(const mint &b) {
*this *= b.inverse();
return *this;
}
constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
constexpr bool operator==(const mint &b) const {
return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
}
constexpr bool operator!=(const mint &b) const {
return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
}
constexpr mint operator-() const { return mint() - mint(*this); }
constexpr mint pow(u64 n) const {
mint ret(1), mul(*this);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
constexpr mint inverse() const { return pow(mod - 2); }
friend ostream &operator<<(ostream &os, const mint &b) {
return os << b.get();
}
friend istream &operator>>(istream &is, mint &b) {
int64_t t;
is >> t;
b = LazyMontgomeryModInt<mod>(t);
return (is);
}
constexpr u32 get() const {
u32 ret = reduce(a);
return ret >= mod ? ret - mod : ret;
}
static constexpr u32 get_mod() { return mod; }
};
__attribute__((target("sse4.2"))) inline __m128i my128_mullo_epu32(
const __m128i &a, const __m128i &b) {
return _mm_mullo_epi32(a, b);
}
__attribute__((target("sse4.2"))) inline __m128i my128_mulhi_epu32(
const __m128i &a, const __m128i &b) {
__m128i a13 = _mm_shuffle_epi32(a, 0xF5);
__m128i b13 = _mm_shuffle_epi32(b, 0xF5);
__m128i prod02 = _mm_mul_epu32(a, b);
__m128i prod13 = _mm_mul_epu32(a13, b13);
__m128i prod = _mm_unpackhi_epi64(_mm_unpacklo_epi32(prod02, prod13),
_mm_unpackhi_epi32(prod02, prod13));
return prod;
}
__attribute__((target("sse4.2"))) inline __m128i montgomery_mul_128(
const __m128i &a, const __m128i &b, const __m128i &r, const __m128i &m1) {
return _mm_sub_epi32(
_mm_add_epi32(my128_mulhi_epu32(a, b), m1),
my128_mulhi_epu32(my128_mullo_epu32(my128_mullo_epu32(a, b), r), m1));
}
__attribute__((target("sse4.2"))) inline __m128i montgomery_add_128(
const __m128i &a, const __m128i &b, const __m128i &m2, const __m128i &m0) {
__m128i ret = _mm_sub_epi32(_mm_add_epi32(a, b), m2);
return _mm_add_epi32(_mm_and_si128(_mm_cmpgt_epi32(m0, ret), m2), ret);
}
__attribute__((target("sse4.2"))) inline __m128i montgomery_sub_128(
const __m128i &a, const __m128i &b, const __m128i &m2, const __m128i &m0) {
__m128i ret = _mm_sub_epi32(a, b);
return _mm_add_epi32(_mm_and_si128(_mm_cmpgt_epi32(m0, ret), m2), ret);
}
__attribute__((target("avx2"))) inline __m256i my256_mullo_epu32(
const __m256i &a, const __m256i &b) {
return _mm256_mullo_epi32(a, b);
}
__attribute__((target("avx2"))) inline __m256i my256_mulhi_epu32(
const __m256i &a, const __m256i &b) {
__m256i a13 = _mm256_shuffle_epi32(a, 0xF5);
__m256i b13 = _mm256_shuffle_epi32(b, 0xF5);
__m256i prod02 = _mm256_mul_epu32(a, b);
__m256i prod13 = _mm256_mul_epu32(a13, b13);
__m256i prod = _mm256_unpackhi_epi64(_mm256_unpacklo_epi32(prod02, prod13),
_mm256_unpackhi_epi32(prod02, prod13));
return prod;
}
__attribute__((target("avx2"))) inline __m256i montgomery_mul_256(
const __m256i &a, const __m256i &b, const __m256i &r, const __m256i &m1) {
return _mm256_sub_epi32(
_mm256_add_epi32(my256_mulhi_epu32(a, b), m1),
my256_mulhi_epu32(my256_mullo_epu32(my256_mullo_epu32(a, b), r), m1));
}
__attribute__((target("avx2"))) inline __m256i montgomery_add_256(
const __m256i &a, const __m256i &b, const __m256i &m2, const __m256i &m0) {
__m256i ret = _mm256_sub_epi32(_mm256_add_epi32(a, b), m2);
return _mm256_add_epi32(_mm256_and_si256(_mm256_cmpgt_epi32(m0, ret), m2),
ret);
}
__attribute__((target("avx2"))) inline __m256i montgomery_sub_256(
const __m256i &a, const __m256i &b, const __m256i &m2, const __m256i &m0) {
__m256i ret = _mm256_sub_epi32(a, b);
return _mm256_add_epi32(_mm256_and_si256(_mm256_cmpgt_epi32(m0, ret), m2),
ret);
}
namespace ntt_inner {
using u64 = uint64_t;
constexpr uint32_t get_pr(uint32_t mod) {
if (mod == 2) return 1;
u64 ds[32] = {};
int idx = 0;
u64 m = mod - 1;
for (u64 i = 2; i * i <= m; ++i) {
if (m % i == 0) {
ds[idx++] = i;
while (m % i == 0) m /= i;
}
}
if (m != 1) ds[idx++] = m;
uint32_t pr = 2;
while (1) {
int flg = 1;
for (int i = 0; i < idx; ++i) {
u64 a = pr, b = (mod - 1) / ds[i], r = 1;
while (b) {
if (b & 1) r = r * a % mod;
a = a * a % mod;
b >>= 1;
}
if (r == 1) {
flg = 0;
break;
}
}
if (flg == 1) break;
++pr;
}
return pr;
}
constexpr int SZ_FFT_BUF = 1 << 23;
uint32_t _buf1[SZ_FFT_BUF] __attribute__((aligned(64)));
uint32_t _buf2[SZ_FFT_BUF] __attribute__((aligned(64)));
} // namespace ntt_inner
template <typename mint>
struct NTT {
static constexpr uint32_t mod = mint::get_mod();
static constexpr uint32_t pr = ntt_inner::get_pr(mint::get_mod());
static constexpr int level = __builtin_ctzll(mod - 1);
mint dw[level], dy[level];
mint *buf1, *buf2;
constexpr NTT() {
setwy(level);
union raw_cast {
mint dat;
uint32_t _;
};
buf1 = &(((raw_cast *)(ntt_inner::_buf1))->dat);
buf2 = &(((raw_cast *)(ntt_inner::_buf2))->dat);
}
constexpr void setwy(int k) {
mint w[level], y[level];
w[k - 1] = mint(pr).pow((mod - 1) / (1 << k));
y[k - 1] = w[k - 1].inverse();
for (int i = k - 2; i > 0; --i)
w[i] = w[i + 1] * w[i + 1], y[i] = y[i + 1] * y[i + 1];
dw[0] = dy[0] = w[1] * w[1];
dw[1] = w[1], dy[1] = y[1], dw[2] = w[2], dy[2] = y[2];
for (int i = 3; i < k; ++i) {
dw[i] = dw[i - 1] * y[i - 2] * w[i];
dy[i] = dy[i - 1] * w[i - 2] * y[i];
}
}
__attribute__((target("avx2"))) void ntt(mint *a, int n) {
int k = n ? __builtin_ctz(n) : 0;
if (k == 0) return;
if (k == 1) {
mint a1 = a[1];
a[1] = a[0] - a[1];
a[0] = a[0] + a1;
return;
}
if (k & 1) {
int v = 1 << (k - 1);
if (v < 8) {
for (int j = 0; j < v; ++j) {
mint ajv = a[j + v];
a[j + v] = a[j] - ajv;
a[j] += ajv;
}
} else {
const __m256i m0 = _mm256_set1_epi32(0);
const __m256i m2 = _mm256_set1_epi32(mod + mod);
int j0 = 0;
int j1 = v;
for (; j0 < v; j0 += 8, j1 += 8) {
__m256i T0 = _mm256_loadu_si256((__m256i *)(a + j0));
__m256i T1 = _mm256_loadu_si256((__m256i *)(a + j1));
__m256i naj = montgomery_add_256(T0, T1, m2, m0);
__m256i najv = montgomery_sub_256(T0, T1, m2, m0);
_mm256_storeu_si256((__m256i *)(a + j0), naj);
_mm256_storeu_si256((__m256i *)(a + j1), najv);
}
}
}
int u = 1 << (2 + (k & 1));
int v = 1 << (k - 2 - (k & 1));
mint one = mint(1);
mint imag = dw[1];
while (v) {
if (v == 1) {
mint ww = one, xx = one, wx = one;
for (int jh = 0; jh < u;) {
ww = xx * xx, wx = ww * xx;
mint t0 = a[jh + 0], t1 = a[jh + 1] * xx;
mint t2 = a[jh + 2] * ww, t3 = a[jh + 3] * wx;
mint t0p2 = t0 + t2, t1p3 = t1 + t3;
mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;
a[jh + 0] = t0p2 + t1p3, a[jh + 1] = t0p2 - t1p3;
a[jh + 2] = t0m2 + t1m3, a[jh + 3] = t0m2 - t1m3;
xx *= dw[__builtin_ctz((jh += 4))];
}
} else if (v == 4) {
const __m128i m0 = _mm_set1_epi32(0);
const __m128i m1 = _mm_set1_epi32(mod);
const __m128i m2 = _mm_set1_epi32(mod + mod);
const __m128i r = _mm_set1_epi32(mint::r);
const __m128i Imag = _mm_set1_epi32(imag.a);
mint ww = one, xx = one, wx = one;
for (int jh = 0; jh < u;) {
if (jh == 0) {
int j0 = 0;
int j1 = v;
int j2 = j1 + v;
int j3 = j2 + v;
int je = v;
for (; j0 < je; j0 += 4, j1 += 4, j2 += 4, j3 += 4) {
const __m128i T0 = _mm_loadu_si128((__m128i *)(a + j0));
const __m128i T1 = _mm_loadu_si128((__m128i *)(a + j1));
const __m128i T2 = _mm_loadu_si128((__m128i *)(a + j2));
const __m128i T3 = _mm_loadu_si128((__m128i *)(a + j3));
const __m128i T0P2 = montgomery_add_128(T0, T2, m2, m0);
const __m128i T1P3 = montgomery_add_128(T1, T3, m2, m0);
const __m128i T0M2 = montgomery_sub_128(T0, T2, m2, m0);
const __m128i T1M3 = montgomery_mul_128(
montgomery_sub_128(T1, T3, m2, m0), Imag, r, m1);
_mm_storeu_si128((__m128i *)(a + j0),
montgomery_add_128(T0P2, T1P3, m2, m0));
_mm_storeu_si128((__m128i *)(a + j1),
montgomery_sub_128(T0P2, T1P3, m2, m0));
_mm_storeu_si128((__m128i *)(a + j2),
montgomery_add_128(T0M2, T1M3, m2, m0));
_mm_storeu_si128((__m128i *)(a + j3),
montgomery_sub_128(T0M2, T1M3, m2, m0));
}
} else {
ww = xx * xx, wx = ww * xx;
const __m128i WW = _mm_set1_epi32(ww.a);
const __m128i WX = _mm_set1_epi32(wx.a);
const __m128i XX = _mm_set1_epi32(xx.a);
int j0 = jh * v;
int j1 = j0 + v;
int j2 = j1 + v;
int j3 = j2 + v;
int je = j1;
for (; j0 < je; j0 += 4, j1 += 4, j2 += 4, j3 += 4) {
const __m128i T0 = _mm_loadu_si128((__m128i *)(a + j0));
const __m128i T1 = _mm_loadu_si128((__m128i *)(a + j1));
const __m128i T2 = _mm_loadu_si128((__m128i *)(a + j2));
const __m128i T3 = _mm_loadu_si128((__m128i *)(a + j3));
const __m128i MT1 = montgomery_mul_128(T1, XX, r, m1);
const __m128i MT2 = montgomery_mul_128(T2, WW, r, m1);
const __m128i MT3 = montgomery_mul_128(T3, WX, r, m1);
const __m128i T0P2 = montgomery_add_128(T0, MT2, m2, m0);
const __m128i T1P3 = montgomery_add_128(MT1, MT3, m2, m0);
const __m128i T0M2 = montgomery_sub_128(T0, MT2, m2, m0);
const __m128i T1M3 = montgomery_mul_128(
montgomery_sub_128(MT1, MT3, m2, m0), Imag, r, m1);
_mm_storeu_si128((__m128i *)(a + j0),
montgomery_add_128(T0P2, T1P3, m2, m0));
_mm_storeu_si128((__m128i *)(a + j1),
montgomery_sub_128(T0P2, T1P3, m2, m0));
_mm_storeu_si128((__m128i *)(a + j2),
montgomery_add_128(T0M2, T1M3, m2, m0));
_mm_storeu_si128((__m128i *)(a + j3),
montgomery_sub_128(T0M2, T1M3, m2, m0));
}
}
xx *= dw[__builtin_ctz((jh += 4))];
}
} else {
const __m256i m0 = _mm256_set1_epi32(0);
const __m256i m1 = _mm256_set1_epi32(mod);
const __m256i m2 = _mm256_set1_epi32(mod + mod);
const __m256i r = _mm256_set1_epi32(mint::r);
const __m256i Imag = _mm256_set1_epi32(imag.a);
mint ww = one, xx = one, wx = one;
for (int jh = 0; jh < u;) {
if (jh == 0) {
int j0 = 0;
int j1 = v;
int j2 = j1 + v;
int j3 = j2 + v;
int je = v;
for (; j0 < je; j0 += 8, j1 += 8, j2 += 8, j3 += 8) {
const __m256i T0 = _mm256_loadu_si256((__m256i *)(a + j0));
const __m256i T1 = _mm256_loadu_si256((__m256i *)(a + j1));
const __m256i T2 = _mm256_loadu_si256((__m256i *)(a + j2));
const __m256i T3 = _mm256_loadu_si256((__m256i *)(a + j3));
const __m256i T0P2 = montgomery_add_256(T0, T2, m2, m0);
const __m256i T1P3 = montgomery_add_256(T1, T3, m2, m0);
const __m256i T0M2 = montgomery_sub_256(T0, T2, m2, m0);
const __m256i T1M3 = montgomery_mul_256(
montgomery_sub_256(T1, T3, m2, m0), Imag, r, m1);
_mm256_storeu_si256((__m256i *)(a + j0),
montgomery_add_256(T0P2, T1P3, m2, m0));
_mm256_storeu_si256((__m256i *)(a + j1),
montgomery_sub_256(T0P2, T1P3, m2, m0));
_mm256_storeu_si256((__m256i *)(a + j2),
montgomery_add_256(T0M2, T1M3, m2, m0));
_mm256_storeu_si256((__m256i *)(a + j3),
montgomery_sub_256(T0M2, T1M3, m2, m0));
}
} else {
ww = xx * xx, wx = ww * xx;
const __m256i WW = _mm256_set1_epi32(ww.a);
const __m256i WX = _mm256_set1_epi32(wx.a);
const __m256i XX = _mm256_set1_epi32(xx.a);
int j0 = jh * v;
int j1 = j0 + v;
int j2 = j1 + v;
int j3 = j2 + v;
int je = j1;
for (; j0 < je; j0 += 8, j1 += 8, j2 += 8, j3 += 8) {
const __m256i T0 = _mm256_loadu_si256((__m256i *)(a + j0));
const __m256i T1 = _mm256_loadu_si256((__m256i *)(a + j1));
const __m256i T2 = _mm256_loadu_si256((__m256i *)(a + j2));
const __m256i T3 = _mm256_loadu_si256((__m256i *)(a + j3));
const __m256i MT1 = montgomery_mul_256(T1, XX, r, m1);
const __m256i MT2 = montgomery_mul_256(T2, WW, r, m1);
const __m256i MT3 = montgomery_mul_256(T3, WX, r, m1);
const __m256i T0P2 = montgomery_add_256(T0, MT2, m2, m0);
const __m256i T1P3 = montgomery_add_256(MT1, MT3, m2, m0);
const __m256i T0M2 = montgomery_sub_256(T0, MT2, m2, m0);
const __m256i T1M3 = montgomery_mul_256(
montgomery_sub_256(MT1, MT3, m2, m0), Imag, r, m1);
_mm256_storeu_si256((__m256i *)(a + j0),
montgomery_add_256(T0P2, T1P3, m2, m0));
_mm256_storeu_si256((__m256i *)(a + j1),
montgomery_sub_256(T0P2, T1P3, m2, m0));
_mm256_storeu_si256((__m256i *)(a + j2),
montgomery_add_256(T0M2, T1M3, m2, m0));
_mm256_storeu_si256((__m256i *)(a + j3),
montgomery_sub_256(T0M2, T1M3, m2, m0));
}
}
xx *= dw[__builtin_ctz((jh += 4))];
}
}
u <<= 2;
v >>= 2;
}
}
__attribute__((target("avx2"))) void intt(mint *a, int n,
int normalize = true) {
int k = n ? __builtin_ctz(n) : 0;
if (k == 0) return;
if (k == 1) {
mint a1 = a[1];
a[1] = a[0] - a[1];
a[0] = a[0] + a1;
if (normalize) {
a[0] *= mint(2).inverse();
a[1] *= mint(2).inverse();
}
return;
}
int u = 1 << (k - 2);
int v = 1;
mint one = mint(1);
mint imag = dy[1];
while (u) {
if (v == 1) {
mint ww = one, xx = one, yy = one;
u <<= 2;
for (int jh = 0; jh < u;) {
ww = xx * xx, yy = xx * imag;
mint t0 = a[jh + 0], t1 = a[jh + 1];
mint t2 = a[jh + 2], t3 = a[jh + 3];
mint t0p1 = t0 + t1, t2p3 = t2 + t3;
mint t0m1 = (t0 - t1) * xx, t2m3 = (t2 - t3) * yy;
a[jh + 0] = t0p1 + t2p3, a[jh + 2] = (t0p1 - t2p3) * ww;
a[jh + 1] = t0m1 + t2m3, a[jh + 3] = (t0m1 - t2m3) * ww;
xx *= dy[__builtin_ctz(jh += 4)];
}
} else if (v == 4) {
const __m128i m0 = _mm_set1_epi32(0);
const __m128i m1 = _mm_set1_epi32(mod);
const __m128i m2 = _mm_set1_epi32(mod + mod);
const __m128i r = _mm_set1_epi32(mint::r);
const __m128i Imag = _mm_set1_epi32(imag.a);
mint ww = one, xx = one, yy = one;
u <<= 2;
for (int jh = 0; jh < u;) {
if (jh == 0) {
int j0 = 0;
int j1 = v;
int j2 = v + v;
int j3 = j2 + v;
for (; j0 < v; j0 += 4, j1 += 4, j2 += 4, j3 += 4) {
const __m128i T0 = _mm_loadu_si128((__m128i *)(a + j0));
const __m128i T1 = _mm_loadu_si128((__m128i *)(a + j1));
const __m128i T2 = _mm_loadu_si128((__m128i *)(a + j2));
const __m128i T3 = _mm_loadu_si128((__m128i *)(a + j3));
const __m128i T0P1 = montgomery_add_128(T0, T1, m2, m0);
const __m128i T2P3 = montgomery_add_128(T2, T3, m2, m0);
const __m128i T0M1 = montgomery_sub_128(T0, T1, m2, m0);
const __m128i T2M3 = montgomery_mul_128(
montgomery_sub_128(T2, T3, m2, m0), Imag, r, m1);
_mm_storeu_si128((__m128i *)(a + j0),
montgomery_add_128(T0P1, T2P3, m2, m0));
_mm_storeu_si128((__m128i *)(a + j2),
montgomery_sub_128(T0P1, T2P3, m2, m0));
_mm_storeu_si128((__m128i *)(a + j1),
montgomery_add_128(T0M1, T2M3, m2, m0));
_mm_storeu_si128((__m128i *)(a + j3),
montgomery_sub_128(T0M1, T2M3, m2, m0));
}
} else {
ww = xx * xx, yy = xx * imag;
const __m128i WW = _mm_set1_epi32(ww.a);
const __m128i XX = _mm_set1_epi32(xx.a);
const __m128i YY = _mm_set1_epi32(yy.a);
int j0 = jh * v;
int j1 = j0 + v;
int j2 = j1 + v;
int j3 = j2 + v;
int je = j1;
for (; j0 < je; j0 += 4, j1 += 4, j2 += 4, j3 += 4) {
const __m128i T0 = _mm_loadu_si128((__m128i *)(a + j0));
const __m128i T1 = _mm_loadu_si128((__m128i *)(a + j1));
const __m128i T2 = _mm_loadu_si128((__m128i *)(a + j2));
const __m128i T3 = _mm_loadu_si128((__m128i *)(a + j3));
const __m128i T0P1 = montgomery_add_128(T0, T1, m2, m0);
const __m128i T2P3 = montgomery_add_128(T2, T3, m2, m0);
const __m128i T0M1 = montgomery_mul_128(
montgomery_sub_128(T0, T1, m2, m0), XX, r, m1);
__m128i T2M3 = montgomery_mul_128(
montgomery_sub_128(T2, T3, m2, m0), YY, r, m1);
_mm_storeu_si128((__m128i *)(a + j0),
montgomery_add_128(T0P1, T2P3, m2, m0));
_mm_storeu_si128(
(__m128i *)(a + j2),
montgomery_mul_128(montgomery_sub_128(T0P1, T2P3, m2, m0), WW,
r, m1));
_mm_storeu_si128((__m128i *)(a + j1),
montgomery_add_128(T0M1, T2M3, m2, m0));
_mm_storeu_si128(
(__m128i *)(a + j3),
montgomery_mul_128(montgomery_sub_128(T0M1, T2M3, m2, m0), WW,
r, m1));
}
}
xx *= dy[__builtin_ctz(jh += 4)];
}
} else {
const __m256i m0 = _mm256_set1_epi32(0);
const __m256i m1 = _mm256_set1_epi32(mod);
const __m256i m2 = _mm256_set1_epi32(mod + mod);
const __m256i r = _mm256_set1_epi32(mint::r);
const __m256i Imag = _mm256_set1_epi32(imag.a);
mint ww = one, xx = one, yy = one;
u <<= 2;
for (int jh = 0; jh < u;) {
if (jh == 0) {
int j0 = 0;
int j1 = v;
int j2 = v + v;
int j3 = j2 + v;
for (; j0 < v; j0 += 8, j1 += 8, j2 += 8, j3 += 8) {
const __m256i T0 = _mm256_loadu_si256((__m256i *)(a + j0));
const __m256i T1 = _mm256_loadu_si256((__m256i *)(a + j1));
const __m256i T2 = _mm256_loadu_si256((__m256i *)(a + j2));
const __m256i T3 = _mm256_loadu_si256((__m256i *)(a + j3));
const __m256i T0P1 = montgomery_add_256(T0, T1, m2, m0);
const __m256i T2P3 = montgomery_add_256(T2, T3, m2, m0);
const __m256i T0M1 = montgomery_sub_256(T0, T1, m2, m0);
const __m256i T2M3 = montgomery_mul_256(
montgomery_sub_256(T2, T3, m2, m0), Imag, r, m1);
_mm256_storeu_si256((__m256i *)(a + j0),
montgomery_add_256(T0P1, T2P3, m2, m0));
_mm256_storeu_si256((__m256i *)(a + j2),
montgomery_sub_256(T0P1, T2P3, m2, m0));
_mm256_storeu_si256((__m256i *)(a + j1),
montgomery_add_256(T0M1, T2M3, m2, m0));
_mm256_storeu_si256((__m256i *)(a + j3),
montgomery_sub_256(T0M1, T2M3, m2, m0));
}
} else {
ww = xx * xx, yy = xx * imag;
const __m256i WW = _mm256_set1_epi32(ww.a);
const __m256i XX = _mm256_set1_epi32(xx.a);
const __m256i YY = _mm256_set1_epi32(yy.a);
int j0 = jh * v;
int j1 = j0 + v;
int j2 = j1 + v;
int j3 = j2 + v;
int je = j1;
for (; j0 < je; j0 += 8, j1 += 8, j2 += 8, j3 += 8) {
const __m256i T0 = _mm256_loadu_si256((__m256i *)(a + j0));
const __m256i T1 = _mm256_loadu_si256((__m256i *)(a + j1));
const __m256i T2 = _mm256_loadu_si256((__m256i *)(a + j2));
const __m256i T3 = _mm256_loadu_si256((__m256i *)(a + j3));
const __m256i T0P1 = montgomery_add_256(T0, T1, m2, m0);
const __m256i T2P3 = montgomery_add_256(T2, T3, m2, m0);
const __m256i T0M1 = montgomery_mul_256(
montgomery_sub_256(T0, T1, m2, m0), XX, r, m1);
const __m256i T2M3 = montgomery_mul_256(
montgomery_sub_256(T2, T3, m2, m0), YY, r, m1);
_mm256_storeu_si256((__m256i *)(a + j0),
montgomery_add_256(T0P1, T2P3, m2, m0));
_mm256_storeu_si256(
(__m256i *)(a + j2),
montgomery_mul_256(montgomery_sub_256(T0P1, T2P3, m2, m0), WW,
r, m1));
_mm256_storeu_si256((__m256i *)(a + j1),
montgomery_add_256(T0M1, T2M3, m2, m0));
_mm256_storeu_si256(
(__m256i *)(a + j3),
montgomery_mul_256(montgomery_sub_256(T0M1, T2M3, m2, m0), WW,
r, m1));
}
}
xx *= dy[__builtin_ctz(jh += 4)];
}
}
u >>= 4;
v <<= 2;
}
if (k & 1) {
v = 1 << (k - 1);
if (v < 8) {
for (int j = 0; j < v; ++j) {
mint ajv = a[j] - a[j + v];
a[j] += a[j + v];
a[j + v] = ajv;
}
} else {
const __m256i m0 = _mm256_set1_epi32(0);
const __m256i m2 = _mm256_set1_epi32(mod + mod);
int j0 = 0;
int j1 = v;
for (; j0 < v; j0 += 8, j1 += 8) {
const __m256i T0 = _mm256_loadu_si256((__m256i *)(a + j0));
const __m256i T1 = _mm256_loadu_si256((__m256i *)(a + j1));
__m256i naj = montgomery_add_256(T0, T1, m2, m0);
__m256i najv = montgomery_sub_256(T0, T1, m2, m0);
_mm256_storeu_si256((__m256i *)(a + j0), naj);
_mm256_storeu_si256((__m256i *)(a + j1), najv);
}
}
}
if (normalize) {
mint invn = mint(n).inverse();
for (int i = 0; i < n; i++) a[i] *= invn;
}
}
__attribute__((target("avx2"))) void inplace_multiply(
int l1, int l2, int zero_padding = true) {
int l = l1 + l2 - 1;
int M = 4;
while (M < l) M <<= 1;
if (zero_padding) {
for (int i = l1; i < M; i++) ntt_inner::_buf1[i] = 0;
for (int i = l2; i < M; i++) ntt_inner::_buf2[i] = 0;
}
const __m256i m0 = _mm256_set1_epi32(0);
const __m256i m1 = _mm256_set1_epi32(mod);
const __m256i r = _mm256_set1_epi32(mint::r);
const __m256i N2 = _mm256_set1_epi32(mint::n2);
for (int i = 0; i < l1; i += 8) {
__m256i a = _mm256_loadu_si256((__m256i *)(ntt_inner::_buf1 + i));
__m256i b = montgomery_mul_256(a, N2, r, m1);
_mm256_storeu_si256((__m256i *)(ntt_inner::_buf1 + i), b);
}
for (int i = 0; i < l2; i += 8) {
__m256i a = _mm256_loadu_si256((__m256i *)(ntt_inner::_buf2 + i));
__m256i b = montgomery_mul_256(a, N2, r, m1);
_mm256_storeu_si256((__m256i *)(ntt_inner::_buf2 + i), b);
}
ntt(buf1, M);
ntt(buf2, M);
for (int i = 0; i < M; i += 8) {
__m256i a = _mm256_loadu_si256((__m256i *)(ntt_inner::_buf1 + i));
__m256i b = _mm256_loadu_si256((__m256i *)(ntt_inner::_buf2 + i));
__m256i c = montgomery_mul_256(a, b, r, m1);
_mm256_storeu_si256((__m256i *)(ntt_inner::_buf1 + i), c);
}
intt(buf1, M, false);
const __m256i INVM = _mm256_set1_epi32((mint(M).inverse()).a);
for (int i = 0; i < l; i += 8) {
__m256i a = _mm256_loadu_si256((__m256i *)(ntt_inner::_buf1 + i));
__m256i b = montgomery_mul_256(a, INVM, r, m1);
__m256i c = my256_mulhi_epu32(my256_mullo_epu32(b, r), m1);
__m256i d = _mm256_and_si256(_mm256_cmpgt_epi32(c, m0), m1);
__m256i e = _mm256_sub_epi32(d, c);
_mm256_storeu_si256((__m256i *)(ntt_inner::_buf1 + i), e);
}
}
void ntt(vector<mint> &a) {
int M = (int)a.size();
for (int i = 0; i < M; i++) buf1[i].a = a[i].a;
ntt(buf1, M);
for (int i = 0; i < M; i++) a[i].a = buf1[i].a;
}
void intt(vector<mint> &a) {
int M = (int)a.size();
for (int i = 0; i < M; i++) buf1[i].a = a[i].a;
intt(buf1, M, true);
for (int i = 0; i < M; i++) a[i].a = buf1[i].a;
}
vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) {
if (a.size() == 0 && b.size() == 0) return vector<mint>{};
int l = a.size() + b.size() - 1;
if (min<int>(a.size(), b.size()) <= 40) {
vector<mint> s(l);
for (int i = 0; i < (int)a.size(); ++i)
for (int j = 0; j < (int)b.size(); ++j) s[i + j] += a[i] * b[j];
return s;
}
assert(l <= ntt_inner::SZ_FFT_BUF);
int M = 4;
while (M < l) M <<= 1;
for (int i = 0; i < (int)a.size(); ++i) buf1[i].a = a[i].a;
for (int i = (int)a.size(); i < M; ++i) buf1[i].a = 0;
for (int i = 0; i < (int)b.size(); ++i) buf2[i].a = b[i].a;
for (int i = (int)b.size(); i < M; ++i) buf2[i].a = 0;
ntt(buf1, M);
ntt(buf2, M);
for (int i = 0; i < M; ++i)
buf1[i].a = mint::reduce(uint64_t(buf1[i].a) * buf2[i].a);
intt(buf1, M, false);
vector<mint> s(l);
mint invm = mint(M).inverse();
for (int i = 0; i < l; ++i) s[i] = buf1[i] * invm;
return s;
}
void ntt_doubling(vector<mint> &a) {
int M = (int)a.size();
for (int i = 0; i < M; i++) buf1[i].a = a[i].a;
intt(buf1, M);
mint r = 1, zeta = mint(pr).pow((mint::get_mod() - 1) / (M << 1));
for (int i = 0; i < M; i++) buf1[i] *= r, r *= zeta;
ntt(buf1, M);
a.resize(2 * M);
for (int i = 0; i < M; i++) a[M + i].a = buf1[i].a;
}
};
namespace ArbitraryNTT {
using i64 = int64_t;
using u128 = __uint128_t;
constexpr int32_t m0 = 167772161;
constexpr int32_t m1 = 469762049;
constexpr int32_t m2 = 754974721;
using mint0 = LazyMontgomeryModInt<m0>;
using mint1 = LazyMontgomeryModInt<m1>;
using mint2 = LazyMontgomeryModInt<m2>;
constexpr int r01 = mint1(m0).inverse().get();
constexpr int r02 = mint2(m0).inverse().get();
constexpr int r12 = mint2(m1).inverse().get();
constexpr int r02r12 = i64(r02) * r12 % m2;
constexpr i64 w1 = m0;
constexpr i64 w2 = i64(m0) * m1;
template <typename T, typename submint>
vector<submint> mul(const vector<T> &a, const vector<T> &b) {
static NTT<submint> ntt;
vector<submint> s(a.size()), t(b.size());
for (int i = 0; i < (int)a.size(); ++i) s[i] = i64(a[i] % submint::get_mod());
for (int i = 0; i < (int)b.size(); ++i) t[i] = i64(b[i] % submint::get_mod());
return ntt.multiply(s, t);
}
template <typename T>
vector<int> multiply(const vector<T> &s, const vector<T> &t, int mod) {
auto d0 = mul<T, mint0>(s, t);
auto d1 = mul<T, mint1>(s, t);
auto d2 = mul<T, mint2>(s, t);
int n = d0.size();
vector<int> ret(n);
const int W1 = w1 % mod;
const int W2 = w2 % mod;
for (int i = 0; i < n; i++) {
int n1 = d1[i].get(), n2 = d2[i].get(), a = d0[i].get();
int b = i64(n1 + m1 - a) * r01 % m1;
int c = (i64(n2 + m2 - a) * r02r12 + i64(m2 - b) * r12) % m2;
ret[i] = (i64(a) + i64(b) * W1 + i64(c) * W2) % mod;
}
return ret;
}
template <typename mint>
vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) {
if (a.size() == 0 && b.size() == 0) return {};
if (min<int>(a.size(), b.size()) < 128) {
vector<mint> ret(a.size() + b.size() - 1);
for (int i = 0; i < (int)a.size(); ++i)
for (int j = 0; j < (int)b.size(); ++j) ret[i + j] += a[i] * b[j];
return ret;
}
vector<int> s(a.size()), t(b.size());
for (int i = 0; i < (int)a.size(); ++i) s[i] = a[i].get();
for (int i = 0; i < (int)b.size(); ++i) t[i] = b[i].get();
vector<int> u = multiply<int>(s, t, mint::get_mod());
vector<mint> ret(u.size());
for (int i = 0; i < (int)u.size(); ++i) ret[i] = mint(u[i]);
return ret;
}
template <typename T>
vector<u128> multiply_u128(const vector<T> &s, const vector<T> &t) {
if (s.size() == 0 && t.size() == 0) return {};
if (min<int>(s.size(), t.size()) < 128) {
vector<u128> ret(s.size() + t.size() - 1);
for (int i = 0; i < (int)s.size(); ++i)
for (int j = 0; j < (int)t.size(); ++j) ret[i + j] += i64(s[i]) * t[j];
return ret;
}
auto d0 = mul<T, mint0>(s, t);
auto d1 = mul<T, mint1>(s, t);
auto d2 = mul<T, mint2>(s, t);
int n = d0.size();
vector<u128> ret(n);
for (int i = 0; i < n; i++) {
i64 n1 = d1[i].get(), n2 = d2[i].get();
i64 a = d0[i].get();
u128 b = (n1 + m1 - a) * r01 % m1;
u128 c = ((n2 + m2 - a) * r02r12 + (m2 - b) * r12) % m2;
ret[i] = a + b * w1 + c * w2;
}
return ret;
}
} // namespace ArbitraryNTT
namespace MultiPrecisionIntegerImpl {
struct TENS {
static constexpr int offset = 30;
constexpr TENS() : _ten(), _tend() {
_ten[0] = 1;
for (int i = 1; i < 20; i++) _ten[i] = _ten[i - 1] * 10;
_tend[offset] = 1;
for (int i = 1; i <= offset; i++) {
_tend[offset + i] = _tend[offset + i - 1] * 10.0;
_tend[offset - i] = 1.0 / _tend[offset + i];
}
}
unsigned long long ten_ull(int n) const {
assert(0 <= n and n < 20);
return _ten[n];
}
long double ten_ld(int n) const {
assert(-offset <= n and n <= offset);
return _tend[n + offset];
}
// 桁数
template <typename I, enable_if_t<is_unsigned_v<I>>* = nullptr>
int digit(I n) const {
int l = 0, r = 20;
while (l + 1 < r) {
int m = (l + r) / 2;
(_ten[m] <= n ? l : r) = m;
}
return l + 1;
}
template <typename I,
enable_if_t<is_signed_v<I> || is_same_v<I, __int128_t>>* = nullptr>
int digit(I n) const {
assert(n >= 0);
return digit((unsigned long long)(n));
}
private:
unsigned long long _ten[20];
long double _tend[offset * 2 + 1];
};
} // namespace MultiPrecisionIntegerImpl
// 0 は neg=false, dat={} として扱う
struct MultiPrecisionInteger {
using M = MultiPrecisionInteger;
inline constexpr static MultiPrecisionIntegerImpl::TENS tens = {};
static constexpr int D = 1000000000;
static constexpr int logD = 9;
bool neg;
vector<int> dat;
MultiPrecisionInteger() : neg(false), dat() {}
MultiPrecisionInteger(bool n, const vector<int>& d) : neg(n), dat(d) {}
template <typename I, enable_if_t<is_integral_v<I> ||
is_same_v<I, __int128_t>>* = nullptr>
MultiPrecisionInteger(I x) : neg(false) {
if constexpr (is_signed_v<I> or is_same_v<I, __int128_t>) {
if (x < 0) neg = true, x = -x;
}
while (x) dat.push_back(x % D), x /= D;
}
MultiPrecisionInteger(const string& S) : neg(false) {
assert(!S.empty());
if (S.size() == 1u and S[0] == '0') return;
int l = 0;
if (S[0] == '-') ++l, neg = true;
for (int ie = S.size(); l < ie; ie -= logD) {
int is = max(l, ie - logD);
long long x = 0;
for (int i = is; i < ie; i++) x = x * 10 + S[i] - '0';
dat.push_back(x);
}
}
friend M operator+(const M& lhs, const M& rhs) {
if (lhs.neg == rhs.neg) return {lhs.neg, _add(lhs.dat, rhs.dat)};
if (_leq(lhs.dat, rhs.dat)) {
// |l| <= |r|
auto c = _sub(rhs.dat, lhs.dat);
bool n = _is_zero(c) ? false : rhs.neg;
return {n, c};
}
auto c = _sub(lhs.dat, rhs.dat);
bool n = _is_zero(c) ? false : lhs.neg;
return {n, c};
}
friend M operator-(const M& lhs, const M& rhs) { return lhs + (-rhs); }
friend M operator*(const M& lhs, const M& rhs) {
auto c = _mul(lhs.dat, rhs.dat);
bool n = _is_zero(c) ? false : (lhs.neg ^ rhs.neg);
return {n, c};
}
friend pair<M, M> divmod(const M& lhs, const M& rhs) {
auto dm = _divmod(lhs.dat, rhs.dat);
bool dn = _is_zero(dm.first) ? false : lhs.neg != rhs.neg;
bool mn = _is_zero(dm.second) ? false : lhs.neg;
return {M{dn, dm.first}, M{mn, dm.second}};
}
friend M operator/(const M& lhs, const M& rhs) {
return divmod(lhs, rhs).first;
}
friend M operator%(const M& lhs, const M& rhs) {
return divmod(lhs, rhs).second;
}
M& operator+=(const M& rhs) { return (*this) = (*this) + rhs; }
M& operator-=(const M& rhs) { return (*this) = (*this) - rhs; }
M& operator*=(const M& rhs) { return (*this) = (*this) * rhs; }
M& operator/=(const M& rhs) { return (*this) = (*this) / rhs; }
M& operator%=(const M& rhs) { return (*this) = (*this) % rhs; }
M operator-() const {
if (is_zero()) return *this;
return {!neg, dat};
}
M operator+() const { return *this; }
friend M abs(const M& m) { return {false, m.dat}; }
bool is_zero() const { return _is_zero(dat); }
friend bool operator==(const M& lhs, const M& rhs) {
return lhs.neg == rhs.neg && lhs.dat == rhs.dat;
}
friend bool operator!=(const M& lhs, const M& rhs) {
return lhs.neg != rhs.neg || lhs.dat != rhs.dat;
}
friend bool operator<(const M& lhs, const M& rhs) {
if (lhs == rhs) return false;
return _neq_lt(lhs, rhs);
}
friend bool operator<=(const M& lhs, const M& rhs) {
if (lhs == rhs) return true;
return _neq_lt(lhs, rhs);
}
friend bool operator>(const M& lhs, const M& rhs) {
if (lhs == rhs) return false;
return _neq_lt(rhs, lhs);
}
friend bool operator>=(const M& lhs, const M& rhs) {
if (lhs == rhs) return true;
return _neq_lt(rhs, lhs);
}
// a * 10^b (1 <= |a| < 10) の形で渡す
// 相対誤差：10^{-16} ~ 10^{-19} 程度 (処理系依存)
pair<long double, int> dfp() const {
if (is_zero()) return {0, 0};
int l = max<int>(0, _size() - 3);
int b = logD * l;
string prefix{};
for (int i = _size() - 1; i >= l; i--) {
prefix += _itos(dat[i], i != _size() - 1);
}
b += prefix.size() - 1;
long double a = 0;
for (auto& c : prefix) a = a * 10.0 + (c - '0');
a *= tens.ten_ld(-prefix.size() + 1);
a = clamp<long double>(a, 1.0, nextafterl(10.0, 1.0));
if (neg) a = -a;
return {a, b};
}
string to_string() const {
if (is_zero()) return "0";
string res;
if (neg) res.push_back('-');
for (int i = _size() - 1; i >= 0; i--) {
res += _itos(dat[i], i != _size() - 1);
}
return res;
}
long double to_ld() const {
auto [a, b] = dfp();
if (-tens.offset <= b and b <= tens.offset) {
return a * tens.ten_ld(b);
}
return a * powl(10, b);
}
long long to_ll() const {
long long res = _to_ll(dat);
return neg ? -res : res;
}
__int128_t to_i128() const {
__int128_t res = _to_i128(dat);
return neg ? -res : res;
}
friend istream& operator>>(istream& is, M& m) {
string s;
is >> s;
m = M{s};
return is;
}
friend ostream& operator<<(ostream& os, const M& m) {
return os << m.to_string();
}
// 内部の関数をテスト
static void _test_private_function(const M&, const M&);
private:
// size
int _size() const { return dat.size(); }
// a == b
static bool _eq(const vector<int>& a, const vector<int>& b) { return a == b; }
// a < b
static bool _lt(const vector<int>& a, const vector<int>& b) {
if (a.size() != b.size()) return a.size() < b.size();
for (int i = a.size() - 1; i >= 0; i--) {
if (a[i] != b[i]) return a[i] < b[i];
}
return false;
}
// a <= b
static bool _leq(const vector<int>& a, const vector<int>& b) {
return _eq(a, b) || _lt(a, b);
}
// a < b (s.t. a != b)
static bool _neq_lt(const M& lhs, const M& rhs) {
assert(lhs != rhs);
if (lhs.neg != rhs.neg) return lhs.neg;
bool f = _lt(lhs.dat, rhs.dat);
if (f) return !lhs.neg;
return lhs.neg;
}
// a == 0
static bool _is_zero(const vector<int>& a) { return a.empty(); }
// a == 1
static bool _is_one(const vector<int>& a) {
return (int)a.size() == 1 and a[0] == 1;
}
// 末尾 0 を削除
static void _shrink(vector<int>& a) {
while (a.size() && a.back() == 0) a.pop_back();
}
// 末尾 0 を削除
void _shrink() {
while (_size() && dat.back() == 0) dat.pop_back();
}
// a + b
static vector<int> _add(const vector<int>& a, const vector<int>& b) {
vector<int> c(max(a.size(), b.size()) + 1);
for (int i = 0; i < (int)a.size(); i++) c[i] += a[i];
for (int i = 0; i < (int)b.size(); i++) c[i] += b[i];
for (int i = 0; i < (int)c.size() - 1; i++) {
if (c[i] >= D) c[i] -= D, c[i + 1]++;
}
_shrink(c);
return c;
}
// a - b
static vector<int> _sub(const vector<int>& a, const vector<int>& b) {
assert(_leq(b, a));
vector<int> c{a};
int borrow = 0;
for (int i = 0; i < (int)a.size(); i++) {
if (i < (int)b.size()) borrow += b[i];
c[i] -= borrow;
borrow = 0;
if (c[i] < 0) c[i] += D, borrow = 1;
}
assert(borrow == 0);
_shrink(c);
return c;
}
// a * b (fft)
static vector<int> _mul_fft(const vector<int>& a, const vector<int>& b) {
if (a.empty() || b.empty()) return {};
auto m = ArbitraryNTT::multiply_u128(a, b);
vector<int> c;
c.reserve(m.size() + 3);
__uint128_t x = 0;
for (int i = 0;; i++) {
if (i >= (int)m.size() && x == 0) break;
if (i < (int)m.size()) x += m[i];
c.push_back(x % D);
x /= D;
}
_shrink(c);
return c;
}
// a * b (naive)
static vector<int> _mul_naive(const vector<int>& a, const vector<int>& b) {
if (a.empty() || b.empty()) return {};
vector<long long> prod(a.size() + b.size() - 1 + 1);
for (int i = 0; i < (int)a.size(); i++) {
for (int j = 0; j < (int)b.size(); j++) {
long long p = 1LL * a[i] * b[j];
prod[i + j + 0] += p % D;
prod[i + j + 1] += p / D;
}
}
vector<int> c;
long long x = 0;
for (int i = 0;; i++) {
if (i >= (int)prod.size() && x == 0) break;
if (i < (int)prod.size()) x += prod[i];
c.push_back(x % D);
x /= D;
}
_shrink(c);
return c;
}
// a * b
static vector<int> _mul(const vector<int>& a, const vector<int>& b) {
if (_is_zero(a) or _is_zero(b)) return {};
if (_is_one(a)) return b;
if (_is_one(b)) return a;
if (min<int>(a.size(), b.size()) <= 128) {
return a.size() < b.size() ? _mul_naive(b, a) : _mul_naive(a, b);
}
return _mul_fft(a, b);
}
// 0 <= A < 1e18, 1 <= B < 1e9
static pair<vector<int>, vector<int>> _divmod_li(const vector<int>& a,
const vector<int>& b) {
assert(0 <= (int)a.size() and (int) a.size() <= 2);
assert((int)b.size() == 1);
long long va = _to_ll(a);
int vb = b[0];
return {_integer_to_vec(va / vb), _integer_to_vec(va % vb)};
}
// 0 <= A < 1e18, 1 <= B < 1e18
static pair<vector<int>, vector<int>> _divmod_ll(const vector<int>& a,
const vector<int>& b) {
assert(0 <= (int)a.size() and (int) a.size() <= 2);
assert(1 <= (int)b.size() and (int) b.size() <= 2);
long long va = _to_ll(a), vb = _to_ll(b);
return {_integer_to_vec(va / vb), _integer_to_vec(va % vb)};
}
// 1 <= B < 1e9
static pair<vector<int>, vector<int>> _divmod_1e9(const vector<int>& a,
const vector<int>& b) {
assert((int)b.size() == 1);
if (b[0] == 1) return {a, {}};
if ((int)a.size() <= 2) return _divmod_li(a, b);
vector<int> quo(a.size());
long long d = 0;
int b0 = b[0];
for (int i = a.size() - 1; i >= 0; i--) {
d = d * D + a[i];
assert(d < 1LL * D * b0);
int q = d / b0, r = d % b0;
quo[i] = q, d = r;
}
_shrink(quo);
return {quo, d ? vector<int>{int(d)} : vector<int>{}};
}
// 0 <= A, 1 <= B
static pair<vector<int>, vector<int>> _divmod(const vector<int>& a,
const vector<int>& b) {
if (_is_zero(b)) {
cerr << "Divide by Zero Exception" << endl;
exit(1);
}
assert(1 <= (int)b.size());
if ((int)b.size() == 1) return _divmod_1e9(a, b);
if (max<int>(a.size(), b.size()) <= 2) return _divmod_ll(a, b);
if (_lt(a, b)) return {{}, a};
// B >= 1e9, A >= B
int norm = D / (b.back() + 1);
vector<int> x = _mul(a, {norm});
vector<int> y = _mul(b, {norm});
int yb = y.back();
vector<int> quo(x.size() - y.size() + 1);
vector<int> rem(x.end() - y.size(), x.end());
for (int i = quo.size() - 1; i >= 0; i--) {
if (rem.size() < y.size()) {
// do nothing
} else if (rem.size() == y.size()) {
if (_leq(y, rem)) {
quo[i] = 1, rem = _sub(rem, y);
}
} else {
assert(y.size() + 1 == rem.size());
long long rb = 1LL * rem[rem.size() - 1] * D + rem[rem.size() - 2];
int q = rb / yb;
vector<int> yq = _mul(y, {q});
// 真の商は q-2 以上 q+1 以下だが自信が無いので念のため while を回す
while (_lt(rem, yq)) q--, yq = _sub(yq, y);
rem = _sub(rem, yq);
while (_leq(y, rem)) q++, rem = _sub(rem, y);
quo[i] = q;
}
if (i) rem.insert(begin(rem), x[i - 1]);
}
_shrink(quo), _shrink(rem);
auto [q2, r2] = _divmod_1e9(rem, {norm});
assert(_is_zero(r2));
return {quo, q2};
}
// int -> string
// 先頭かどうかに応じて zero padding するかを決める
static string _itos(int x, bool zero_padding) {
assert(0 <= x and x < D);
string res;
for (int i = 0; i < logD; i++) {
res.push_back('0' + x % 10), x /= 10;
}
if (!zero_padding) {
while (res.size() && res.back() == '0') res.pop_back();
assert(!res.empty());
}
reverse(begin(res), end(res));
return res;
}
// convert ll to vec
template <typename I, enable_if_t<is_integral_v<I> ||
is_same_v<I, __int128_t>>* = nullptr>
static vector<int> _integer_to_vec(I x) {
if constexpr (is_signed_v<I> or is_same_v<I, __int128_t>) {
assert(x >= 0);
}
vector<int> res;
while (x) res.push_back(x % D), x /= D;
return res;
}
static long long _to_ll(const vector<int>& a) {
long long res = 0;
for (int i = (int)a.size() - 1; i >= 0; i--) res = res * D + a[i];
return res;
}
static __int128_t _to_i128(const vector<int>& a) {
__int128_t res = 0;
for (int i = (int)a.size() - 1; i >= 0; i--) res = res * D + a[i];
return res;
}
static void _dump(const vector<int>& a, string s = "") {
if (!s.empty()) cerr << s << " : ";
cerr << "{ ";
for (int i = 0; i < (int)a.size(); i++) cerr << a[i] << ", ";
cerr << "}" << endl;
}
};
using bigint = MultiPrecisionInteger;
/**
* @brief 多倍長整数
*/
namespace GarnerImpl {
template <typename T>
constexpr T safe_mod(T x, T m) {
x %= m;
if (x < 0) x += m;
return x;
}
template <typename T>
constexpr std::pair<T, T> inv_gcd(T a, T b) {
a = safe_mod(a, b);
if (a == 0) return {b, 0};
T s = b, t = a;
T m0 = 0, m1 = 1;
while (t) {
T 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};
}
template <typename T>
T inv_mod(T x, T m) {
assert(1 <= m);
auto z = inv_gcd(x, m);
assert(z.first == 1);
return z.second;
}
bigint garner_bigint(const vector<long long>& a, const vector<long long>& m) {
int ms = a.size();
vector<long long> coffs(ms, 1), constants(ms), digs(ms);
for (int i = 0; i < ms; ++i) {
long long v = (a[i] - constants[i]) * inv_mod(coffs[i], m[i]) % m[i];
if (v < 0) v += m[i];
digs[i] = v;
for (int j = i + 1; j < ms; j++) {
constants[j] += coffs[j] * v;
constants[j] %= m[j];
coffs[j] *= m[i];
coffs[j] %= m[j];
}
}
bigint ans = bigint{0}, c = bigint{1};
for (int i = ms - 1; i >= 0; --i) {
c *= bigint{m[i]};
ans *= bigint{m[i]};
ans += bigint{digs[i]};
}
if (ans > c / 2) ans -= c;
if (ans < 0) ans += c;
return ans;
}
bigint crt_bigint(const vector<long long>& a, const vector<long long>& m) {
return garner_bigint(a, m);
}
} // namespace Garner
using GarnerImpl::crt_bigint;
using GarnerImpl::garner_bigint;
//
template <typename T, int H, int W>
struct Matrix {
using Array = array<array<T, W>, H>;
Array A;
Matrix() : A() {
for (int i = 0; i < H; i++)
for (int j = 0; j < W; j++) (*this)[i][j] = T();
}
int height() const { return H; }
int width() const { return W; }
inline const array<T, W> &operator[](int k) const { return A[k]; }
inline array<T, W> &operator[](int k) { return A[k]; }
static Matrix I() {
assert(H == W);
Matrix mat;
for (int i = 0; i < H; i++) mat[i][i] = 1;
return (mat);
}
Matrix &operator+=(const Matrix &B) {
for (int i = 0; i < H; i++)
for (int j = 0; j < W; j++) A[i][j] += B[i][j];
return (*this);
}
Matrix &operator-=(const Matrix &B) {
for (int i = 0; i < H; i++)
for (int j = 0; j < W; j++) A[i][j] -= B[i][j];
return (*this);
}
Matrix &operator*=(const Matrix &B) {
assert(H == W);
Matrix C;
for (int i = 0; i < H; i++)
for (int k = 0; k < H; k++)
for (int j = 0; j < H; j++) C[i][j] += A[i][k] * B[k][j];
A.swap(C.A);
return (*this);
}
Matrix &operator^=(long long k) {
Matrix B = Matrix::I();
while (k > 0) {
if (k & 1) B *= *this;
*this *= *this;
k >>= 1LL;
}
A.swap(B.A);
return (*this);
}
Matrix operator+(const Matrix &B) const { return (Matrix(*this) += B); }
Matrix operator-(const Matrix &B) const { return (Matrix(*this) -= B); }
Matrix operator*(const Matrix &B) const { return (Matrix(*this) *= B); }
Matrix operator^(const long long k) const { return (Matrix(*this) ^= k); }
bool operator==(const Matrix &B) const {
for (int i = 0; i < H; i++)
for (int j = 0; j < W; j++)
if (A[i][j] != B[i][j]) return false;
return true;
}
bool operator!=(const Matrix &B) const {
for (int i = 0; i < H; i++)
for (int j = 0; j < W; j++)
if (A[i][j] != B[i][j]) return true;
return false;
}
friend ostream &operator<<(ostream &os,const Matrix &p) {
for (int i = 0; i < H; i++) {
os << "[";
for (int j = 0; j < W; j++) {
os << p[i][j] << (j + 1 == W ? "]\n" : ",");
}
}
return (os);
}
T determinant(int n = -1) {
if (n == -1) n = H;
Matrix B(*this);
T ret = 1;
for (int i = 0; i < n; i++) {
int idx = -1;
for (int j = i; j < n; j++) {
if (B[j][i] != 0) {
idx = j;
break;
}
}
if (idx == -1) return 0;
if (i != idx) {
ret *= T(-1);
swap(B[i], B[idx]);
}
ret *= B[i][i];
T inv = T(1) / B[i][i];
for (int j = 0; j < n; j++) {
B[i][j] *= inv;
}
for (int j = i + 1; j < n; j++) {
T a = B[j][i];
if (a == 0) continue;
for (int k = i; k < n; k++) {
B[j][k] -= B[i][k] * a;
}
}
}
return (ret);
}
};
/**
* @brief 行列ライブラリ(std::array版)
*/
using namespace Nyaan;
using Mat = Matrix<bigint, 2, 2>;
// a^n
template <typename T, typename U>
T power(
const T& a, U n, const T& I,
const function<T(const T&, const T&)>& f = [](const T& s, const T& t) {
return s * t;
}) {
assert(n >= 0);
if (n == 0) return I;
T half = power(a, n / 2, I, f);
T res = f(half, half);
return n % 2 ? f(res, a) : res;
}
void Nyaan::solve() {
int l;
cin >> l;
if (l == 2) die("3\nINF");
cout << l << endl;
Mat A, I;
A[0][0] = A[0][1] = A[1][0] = 1;
I[0][0] = I[1][1] = 1;
// trc(A);
// trc(I);
// trc(power(A, l, I));
if (l & 1) {
cout << power(A, l, I)[1][0] << endl;
} else {
auto B = power(A, l / 2, I);
auto X = (B * B)[1][0];
auto Y = B[1][0];
cout << X - Y * Y << endl;
}
}