結果
問題 | No.1100 Boxes |
ユーザー |
![]() |
提出日時 | 2020-06-26 21:54:43 |
言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 95 ms / 2,000 ms |
コード長 | 4,820 bytes |
コンパイル時間 | 1,989 ms |
コンパイル使用メモリ | 178,088 KB |
実行使用メモリ | 7,788 KB |
最終ジャッジ日時 | 2024-07-04 20:56:34 |
合計ジャッジ時間 | 3,917 ms |
ジャッジサーバーID (参考情報) |
judge1 / judge3 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 4 |
other | AC * 36 |
ソースコード
#include <bits/stdc++.h>int ri() {int n;scanf("%d", &n);return n;}template<int mod, int proot> struct NTT {int get_mod() { return mod; }int pow(int a, int b) {int res = 1;for (; b; b >>= 1) {if (b & 1) res = (int64_t) res * a % mod;a = (int64_t) a * a % mod;}return res;}int inv(int i) { return pow(i, mod - 2); }void ntt(std::vector<int> &a, bool inverse) {int n = a.size();assert((n & -n) == n);int h = pow(proot, (mod - 1) / n);if (inverse) h = inv(h);for (int i = 0, j = 1; j < n - 1; j++) {for (int k = n >> 1; k > (i ^= k); k >>= 1);if (j < i) std::swap(a[i], a[j]);}for (int i = 1; i < n; i <<= 1) {int base = pow(h, n / i / 2);int w = 1;std::vector<int> ws(i);for (int j = 0; j < i; j++) ws[j] = w, w = (int64_t) w * base % mod;for (int j = 0; j < n; j += i << 1) {for (int k = 0; k < i; k++) {int u = a[k + j];int d = (int64_t) a[k + j + i] * ws[k] % mod;a[k + j] = u + d >= mod ? u + d - mod : u + d;a[k + j + i] = d > u ? u + mod - d : u - d;}}}if (inverse) {int ninv = inv(a.size());for (auto &i : a) i = (int64_t) i * ninv % mod;}}std::vector<int> conv(const std::vector<int> &a_, const std::vector<int> &b_) {if (!a_.size() || !b_.size()) return {};std::vector<int> a = a_, b = b_;size_t size = 1;for (; size < a_.size() + b_.size(); size <<= 1);a.resize(size);b.resize(size);ntt(a, false);ntt(b, false);for (size_t i = 0; i < size; i++) a[i] = (int64_t) a[i] * b[i] % mod;ntt(a, true);a.resize(a_.size() + b_.size() - 1);return a;}std::vector<int> self_conv(std::vector<int> a) {if (!a.size()) return {};size_t n_ = a.size();size_t size = 1;for (; size < n_ + n_; size <<= 1);a.resize(size);ntt(a, false);for (auto &i : a) i = (int64_t) i * i % mod;ntt(a, true);a.resize(n_ + n_ - 1);return a;}};template<int mod>struct ModInt{int x;ModInt () : x(0) {}ModInt (int64_t x) : x(x >= 0 ? x % mod : (mod - -x % mod) % mod) {}ModInt &operator += (const ModInt &p){if ((x += p.x) >= mod) x -= mod;return *this;}ModInt &operator -= (const ModInt &p) {if ((x += mod - p.x) >= mod) x -= mod;return *this;}ModInt &operator *= (const ModInt &p) {x = (int64_t) x * p.x % mod;return *this;}ModInt &operator /= (const ModInt &p) {*this *= p.inverse();return *this;}ModInt &operator ^= (int64_t p) {ModInt res = 1;for (; p; p >>= 1) {if (p & 1) res *= *this;*this *= *this;}return *this = res;}ModInt operator - () const { return ModInt(-x); }ModInt operator + (const ModInt &p) const { return ModInt(*this) += p; }ModInt operator - (const ModInt &p) const { return ModInt(*this) -= p; }ModInt operator * (const ModInt &p) const { return ModInt(*this) *= p; }ModInt operator / (const ModInt &p) const { return ModInt(*this) /= p; }ModInt operator ^ (int64_t p) const { return ModInt(*this) ^= p; }bool operator == (const ModInt &p) const { return x == p.x; }bool operator != (const ModInt &p) const { return x != p.x; }explicit operator int() const { return x; }ModInt &operator = (const int p) { x = p; return *this;}ModInt inverse() const {int a = x, b = mod, u = 1, v = 0, t;while (b > 0) {t = a / b;a -= t * b;std::swap(a, b);u -= t * v;std::swap(u, v);}return ModInt(u);}friend std::ostream & operator << (std::ostream &stream, const ModInt<mod> &p) {return stream << p.x;}friend std::istream & operator >> (std::istream &stream, ModInt<mod> &a) {int64_t x;stream >> x;a = ModInt<mod>(x);return stream;}};template<int mod> struct MComb {using mint = ModInt<mod>;std::vector<mint> fact;std::vector<mint> inv;MComb (int n) { // O(n + log(mod))fact = std::vector<mint>(n + 1, 1);for (int i = 1; i <= n; i++) fact[i] = fact[i - 1] * mint(i);inv.resize(n + 1);inv[n] = fact[n] ^ (mod - 2);for (int i = n; i--; ) inv[i] = inv[i + 1] * mint(i + 1);}mint ncr(int n, int r) {return fact[n] * inv[r] * inv[n - r];}mint npr(int n, int r) {return fact[n] * inv[n - r];}mint nhr(int n, int r) {assert(n + r - 1 < (int) fact.size());return ncr(n + r - 1, r);}};#define MOD 998244353typedef ModInt<MOD> mint;int main() {int n = ri();int k = ri();MComb<998244353> com(k);std::vector<int> r0(k + 1);std::vector<int> r1(k + 1);for (int i = 0; i <= k; i++) r0[i] = (int) ((mint(i) ^ n) / com.fact[i]);for (int i = 0; i <= k; i++) r1[i] = (int) ((mint(-1) ^ i) / com.fact[i]);auto tmp = NTT<998244353, 3>().conv(r0, r1);mint res = 0;for (int i = 1; i <= k; i += 2) res += mint(tmp[k - i]) * com.fact[k - i] * com.ncr(k, i);std::cout << res << std::endl;return 0;}