結果

問題 No.2459 Stampaholic (Hard)
ユーザー SSRS
提出日時 2023-09-01 22:35:15
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 2,603 ms / 4,000 ms
コード長 3,502 bytes
コンパイル時間 4,084 ms
コンパイル使用メモリ 236,456 KB
最終ジャッジ日時 2025-02-16 16:58:44
ジャッジサーバーID
(参考情報)
judge2 / judge3
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 3
other AC * 19
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#include <bits/stdc++.h>
#include <atcoder/convolution>
using namespace std;
const long long MOD = 998244353;
long long modpow(long long a, long long b){
long long ans = 1;
while (b > 0){
if (b % 2 == 1){
ans *= a;
ans %= MOD;
}
a *= a;
a %= MOD;
b /= 2;
}
return ans;
}
long long modinv(long long a){
return modpow(a, MOD - 2);
}
vector<long long> inverse(vector<long long> f){
int N = f.size();
vector<long long> ans(1);
ans[0] = 1;
for (int i = 1; i < N * 2; i *= 2){
vector<long long> ans2 = ans;
ans2.resize(i * 4);
int N2 = min(N, i * 2);
vector<long long> f2(i * 4, 0);
for (int j = 0; j < N2; j++){
f2[j] = f[j];
}
ans2 = atcoder::convolution(ans2, ans2);
ans2.resize(i * 2);
ans2 = atcoder::convolution(ans2, f2);
ans2.resize(i * 2);
for (int j = 0; j < i; j++){
ans2[j] = MOD - ans2[j] + ans[j] * 2;
ans2[j] %= MOD;
}
swap(ans, ans2);
}
ans.resize(N);
return ans;
}
int main(){
int H, W, N, K;
cin >> H >> W >> N >> K;
vector<long long> inv(N + 2);
inv[1] = 1;
for (int i = 2; i <= N + 1; i++){
inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
}
vector<long long> fact(N + 2);
vector<long long> finv(N + 2);
fact[0] = 1;
finv[0] = 1;
for (int i = 1; i <= N + 1; i++){
fact[i] = fact[i - 1] * i % MOD;
finv[i] = finv[i - 1] * inv[i] % MOD;
}
vector<long long> binom(N + 1);
for (int i = 0; i <= N; i++){
binom[i] = fact[N] * finv[i] % MOD * finv[N - i] % MOD;
}
int px = min(H - K + 1, K);
int py = min(W - K + 1, K);
int qx = H - 2 * (px - 1);
int qy = W - 2 * (py - 1);
long long C = MOD - modinv(H - K + 1) * modinv(W - K + 1) % MOD;
vector<long long> POW_C(N + 1);
vector<long long> POW_Cpx(N + 1);
vector<long long> POW_Cpy(N + 1);
POW_C[0] = 1;
POW_Cpx[0] = 1;
POW_Cpy[0] = 1;
for (int i = 0; i < N; i++){
POW_C[i + 1] = POW_C[i] * C % MOD;
POW_Cpx[i + 1] = POW_Cpx[i] * C % MOD * px % MOD;
POW_Cpy[i + 1] = POW_Cpy[i] * C % MOD * py % MOD;
}
auto solve = [&](long long N, int K){
vector<long long> POW_N(K + 2);
POW_N[0] = 1;
for (int i = 0; i < K + 1; i++){
POW_N[i + 1] = POW_N[i] * N % MOD;
}
vector<long long> num(K + 1, 0);
for (int i = 0; i <= K; i++){
num[i] = POW_N[i + 1] * finv[i + 1] % MOD;
}
vector<long long> den(K + 1, 0);
for (int i = 0; i <= K; i++){
den[i] = finv[i + 1];
}
vector<long long> den_inv = inverse(den);
vector<long long> ans = atcoder::convolution(num, den_inv);
for (int i = 0; i <= K; i++){
ans[i] *= fact[i];
ans[i] %= MOD;
}
ans[0]--;
return ans;
};
vector<long long> sum_px = solve(px, N);
vector<long long> sum_py = solve(py, N);
long long ans1 = 0;
for (int i = 0; i <= N; i++){
ans1 += POW_C[i] * binom[i] % MOD * sum_px[i] % MOD * sum_py[i] % MOD;
}
ans1 %= MOD;
ans1 *= 4;
ans1 %= MOD;
long long ans2 = 0;
for (int i = 0; i <= N; i++){
ans2 += POW_Cpy[i] * binom[i] % MOD * sum_px[i] % MOD;
}
ans2 %= MOD;
ans2 *= 2 * qy;
ans2 %= MOD;
long long ans3 = 0;
for (int i = 0; i <= N; i++){
ans3 += POW_Cpx[i] * binom[i] % MOD * sum_py[i] % MOD;
}
ans3 %= MOD;
ans3 *= 2 * qx;
ans3 %= MOD;
long long ans4 = modpow(MOD + 1 + C * px % MOD * py % MOD, N) * qx % MOD * qy % MOD;
long long ans = (ans1 + ans2 + ans3 + ans4) % MOD;
cout << ((long long) H * W % MOD - ans + MOD) % MOD << endl;
}
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