結果
問題 | No.1100 Boxes |
ユーザー |
|
提出日時 | 2020-06-26 22:12:01 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 78 ms / 2,000 ms |
コード長 | 3,362 bytes |
コンパイル時間 | 2,102 ms |
コンパイル使用メモリ | 200,720 KB |
最終ジャッジ日時 | 2025-01-11 11:37:28 |
ジャッジサーバーID (参考情報) |
judge5 / 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 <bits/stdc++.h>using namespace std;const int64_t MOD = 998244353;const int64_t ROOT = 3;// MOD-1が何回2で割れるかconst int MX_PW = 23;void add(int64_t& a, int64_t b){a = (a+b) % MOD;}void mul(int64_t& a, int64_t b){a = a*b % MOD;}int64_t power_mod(int64_t num, int64_t power){int64_t prod = 1;num %= MOD;while(power > 0){if(power&1) prod = prod * num % MOD;num = num * num % MOD;power >>= 1;}return prod;}int64_t extgcd(int64_t a, int64_t b, int64_t& x, int64_t& y){int64_t d = a;if(b != 0){d = extgcd(b, a%b, y, x);y -= (a/b) * x;}else{x = 1; y = 0;}return d;}int64_t inv_mod(int64_t a){int64_t x, y;extgcd(a, MOD, x, y);return (MOD + x%MOD) % MOD;}vector<int64_t> zeta, zeta_inv;void prepare_ntt(){zeta.resize(MX_PW);zeta_inv.resize(MX_PW);zeta[MX_PW-1] = power_mod(ROOT, (MOD-1)/(1<<MX_PW));zeta_inv[MX_PW-1] = inv_mod(zeta[MX_PW-1]);for(int k=MX_PW-2; k>=0; k--){zeta[k] = zeta[k+1] * zeta[k+1] % MOD;zeta_inv[k] = zeta_inv[k+1] * zeta_inv[k+1] % MOD;}}void dft(vector<int64_t>& f, int n, bool inverse){if(n==1) return;int c = 0;for(int i=1; i<n; i++){for(int j=(n>>1); j>(c^=j); j>>=1);if(c > i){swap(f[c], f[i]);}}for(int i=1, k=0; i<n; i<<=1, k++){int64_t w = (inverse ? zeta_inv[k] : zeta[k]);for(int j=0; j<n; j+=2*i){int64_t wn = 1;for(int k=0; k<i; k++){int64_t u = f[k+j];int64_t v = f[k+j+i] * wn % MOD;f[k+j] = (u+v) % MOD;f[k+j+i] = (u-v+MOD) % MOD;wn = wn * w % MOD;}}}}vector<int64_t> convolution(vector<int64_t> f, vector<int64_t> g, bool truncate=true){if(zeta.size() == 0) prepare_ntt();int sz = f.size() + g.size();int n = 1;while(n <= sz) n <<= 1;f.resize(n);g.resize(n);dft(f, n, false);dft(g, n, false);vector<int64_t> h(n);for(int i=0; i<n; i++) h[i] = f[i] * g[i] % MOD;dft(h, n, true);int64_t ninv = inv_mod(n);for(int64_t& a : h) mul(a, ninv);if(truncate) while(h.size() && h.back() == 0) h.pop_back();return h;}vector<int64_t> fact, fact_inv;void create_mod_tables(int num){fact.assign(num+1, 1);fact_inv.assign(num+1, 1);for(int i=1; i<=num; i++) fact[i] = fact[i-1] * i % MOD;fact_inv[num] = inv_mod(fact[num]);for(int i=num; i>0; i--) fact_inv[i-1] = fact_inv[i] * i % MOD;}int64_t comb_mod(int n, int k){return fact[n] * fact_inv[n-k] % MOD * fact_inv[k] % MOD;}int64_t perm_mod(int n, int k){return fact[n] * fact_inv[n-k] % MOD;}int main(){int N, K;cin >> N >> K;create_mod_tables(K+1);vector<int64_t> VA(K+1), VI(K+1);for(int a=1; a<=K; a+=2) VA[a] = fact_inv[a];for(int i=0; i<=K; i++){VI[i] = fact_inv[i] * power_mod(i, N) % MOD;if(i%2) VI[i] = (MOD-VI[i]) % MOD;}auto res = convolution(VA, VI);int64_t ans = 0;for(int i=0; i<=K; i++){add(ans, res[i] * fact_inv[K-i]);}mul(ans, fact[K]);if(K%2 == 0) ans = (MOD-ans) % MOD;cout << ans << endl;return 0;}