結果

問題 No.1100 Boxes
ユーザー betrue12
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
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 4
other AC * 36
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>
using namespace std;
const int64_t MOD = 998244353;
const int64_t ROOT = 3;
// MOD-12
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;
}
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