結果
問題 | No.1100 Boxes |
ユーザー |
![]() |
提出日時 | 2020-06-26 23:08:11 |
言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 87 ms / 2,000 ms |
コード長 | 6,242 bytes |
コンパイル時間 | 1,339 ms |
コンパイル使用メモリ | 124,380 KB |
実行使用メモリ | 16,360 KB |
最終ジャッジ日時 | 2024-07-04 23:34:32 |
合計ジャッジ時間 | 3,600 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge2 |
(要ログイン)
ファイルパターン | 結果 |
---|---|
sample | AC * 4 |
other | AC * 36 |
ソースコード
#include <iostream>#include <vector>#include <algorithm>#include <cmath>#include <string>#include <queue>#include <stack>#include <set>#include <map>#include <iomanip>#include <utility>#include <tuple>#include <functional>#include <bitset>#include <cassert>#include <complex>#include <stdio.h>#include <time.h>#include <numeric>#include <random>#include <unordered_map>#include <unordered_set>#define all(a) a.begin(),a.end()#define rep(i, n) for (ll i = 0; i < (n); i++)#define pb push_back#pragma GCC optimize("O3")#pragma GCC optimize("unroll-loops")using namespace std;typedef long long ll;typedef unsigned long long ull;typedef long double ld;typedef pair<ll, ll> P;typedef complex<ld> com;constexpr int inf = 1000000010;constexpr ll INF = 1000000000000000010;constexpr ld eps = 1e-12;constexpr ld pi = 3.141592653589793238;template<class T, class U> inline bool chmax(T &a, const U &b) { if (a < b) { a = b; return true; } return false; }template<class T, class U> inline bool chmin(T &a, const U &b) { if (a > b) { a = b; return true; } return false; }constexpr ll mod = 998244353;constexpr ll modsize = 200000;vector<ll> fac(modsize);vector<ll> inv(modsize);vector<ll> facinv(modsize);void modcalc() {if (modsize == 0) abort();fac[0] = 1; fac[1] = 1; inv[1] = 1;facinv[0] = 1; facinv[1] = 1;for (ll i = 2; i < modsize; i++) {fac[i] = fac[i - 1] * i % mod;inv[i] = mod - inv[mod % i] * (mod / i) % mod;facinv[i] = facinv[i - 1] * inv[i] % mod;}}ll modinv(ll a) {if (a == 0) abort();ll b = mod, u = 1, v = 0;while (b) {ll t = a / b;a -= t * b; swap(a, b);u -= t * v; swap(u, v);}u %= mod;if (u < 0) u += mod;return u;}ll modpow(ll a, ll b) {ll ans = 1;a %= mod;while (b) {if (b & 1) ans = ans * a % mod;a = a * a % mod;b >>= 1;}return ans;}ll modcomb(ll n, ll k) {if (n < 0 || k < 0 || n < k) return 0;return fac[n] * facinv[k] % mod * facinv[n - k] % mod;}ll modperm(ll n, ll k) {if (n < 0 || k < 0 || n < k) return 0;return fac[n] * facinv[n - k] % mod;}ll modhom(ll n, ll k) {if (n < 0 || k < 0 || n == 0 && k > 0) return 0;if (n == 0 && k == 0) return 1;return fac[n + k - 1] * facinv[k] % mod * facinv[n - 1] % mod;}template<int mod, int root = 3> class NumberTheoreticTransform {inline static constexpr long long gcd(long long a, long long b) {return (b ? gcd(b, a % b) : a);}inline static long long ext_gcd(long long a, long long b, long long &x, long long &y) {long long res;if (b == 0) res = a, x = 1, y = 0;else res = ext_gcd(b, a%b, y, x), y -= a / b * x;return res;}inline static long long inv_mod(long long a, long long b) {long long x, y;ext_gcd(a, b, x, y);return (x%b + b) % b;}inline static long long pow_mod(long long x, long long n, long long m) {long long res = 1;for (; n > 0; n >>= 1, (x *= x) %= m) if (n & 1) (res *= x) %= m;return res;}inline static long long garner(vector<long long> b, vector<long long> m, long long d) {int N = b.size();vector<long long> coe(N + 1, 1), val(N + 1, 0);long long g, gl, gr, sum = accumulate(b.begin(), b.end(), 0LL);for (int l = 0; l < N; ++l) {for (int r = l + 1; r < N; ++r) {g = gcd(m[l], m[r]);if (sum && (b[l] - b[r]) % g != 0) return -1;m[l] /= g, m[r] /= g;gl = gcd(m[l], g), gr = g / gl;do {g = gcd(gl, gr);gl *= g, gr /= g;} while (g != 1);m[l] *= gl, m[r] *= gr;b[l] %= m[l], b[r] %= m[r];}}if (!sum) {long long lcm = 1;for (auto& e : m) (lcm *= e) %= d;return lcm;}m.push_back(d);for (int i = 0; i < N; ++i) {long long t = (b[i] - val[i]) * inv_mod(coe[i], m[i]);((t %= m[i]) += m[i]) %= m[i];for (int j = i + 1; j <= N; ++j) {(val[j] += t * coe[j]) %= m[j];(coe[j] *= m[i]) %= m[j];}}return val.back();}inline static void ntt(vector<long long>& f, int sgn = 1) {int N = f.size();int h = pow_mod(root, (mod - 1) / N, mod);if (sgn == -1) h = inv_mod(h, mod);for (int i = 0, j = 1; j < N - 1; ++j) {for (int k = N >> 1; k > (i ^= k); k >>= 1);if (j < i) swap(f[i], f[j]);}for (int i = 1, j = 2; i < N; i *= 2, j *= 2) {long long w = 1, base = pow_mod(h, N / j, mod);for (int k = 0; k < i; ++k, (w *= base) %= mod) {for (int l = k; l < N; l += j) {long long u = f[l];long long d = f[l + i] * w % mod;f[l] = u + d;if (f[l] >= mod) f[l] -= mod;f[l + i] = u - d;if (f[l + i] < 0) f[l + i] += mod;}}}for (auto& x : f) if (x < 0) x += mod;}public:inline static vector<long long> convolution(vector<long long> g, vector<long long> h) {int N; for (N = 1; N < g.size() + h.size(); N *= 2);vector<long long> f(N);g.resize(N); h.resize(N);ntt(g); ntt(h);for (int i = 0; i < N; ++i) (f[i] = g[i] * h[i]) %= mod;ntt(f, -1);long long inv = inv_mod(N, mod);for (auto& x : f) x = x * inv % mod;return f;}inline static vector<long long> convolution_arbitrarymod(vector<long long> g, vector<long long> h) {for (auto& a : g) a %= mod;for (auto& a : h) a %= mod;const int mod1 = 167772161;const int mod2 = 469762049;const int mod3 = 1224736769;auto x = NumberTheoreticTransform<mod1>::convolution(g, h);auto y = NumberTheoreticTransform<mod2>::convolution(g, h);auto z = NumberTheoreticTransform<mod3>::convolution(g, h);vector<long long> res(x.size()), b(3), m(3);for (int i = 0; i < x.size(); ++i) {m[0] = mod1, b[0] = x[i];m[1] = mod2, b[1] = y[i];m[2] = mod3, b[2] = z[i];res[i] = garner(b, m, mod);}return res;}};signed main() {cin.tie(0);ios::sync_with_stdio(false);cout << fixed << setprecision(20);modcalc();ll n, k;cin >> n >> k;vector<ll> a(k + 1), b(k + 1);rep(i, k + 1) {if (i & 1) b[i] = facinv[i];if ((k & 1) != (i & 1)) a[i] = modpow(i, n) * facinv[i] % mod;else {a[i] = mod - modpow(i, n) * facinv[i] % mod;if (a[i] >= mod) a[i] -= mod;}}vector<ll> c = NumberTheoreticTransform<998244353>::convolution(a, b);ll ans = 0;rep(i, k + 1) ans += c[i] * facinv[k - i] % mod;ans %= mod;cout << ans * fac[k] % mod << '\n';}