結果

問題 No.1100 Boxes
ユーザー 増井舜
提出日時 2020-06-27 13:59:49
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,895 ms / 2,000 ms
コード長 4,296 bytes
コンパイル時間 1,888 ms
コンパイル使用メモリ 174,764 KB
実行使用メモリ 162,948 KB
最終ジャッジ日時 2024-07-05 09:06:32
合計ジャッジ時間 18,289 ms
ジャッジサーバーID
(参考情報)
judge3 / judge5
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"
#include<vector>
#include<iostream>
#include<queue>
#include<algorithm>
#include<map>
#include<set>
#include<iomanip>
#include<assert.h>
#include<unordered_map>
#include<unordered_set>
#include<string>
#include<stack>
#include<complex>
#include<memory>
#pragma warning(disable:4996)
using namespace std;
using ld = long double;
template<class T>
using Table = vector<vector<T>>;
const ld eps=1e-9;
using Graph=vector<vector<int>>;
using ll=long long;
#define WHATS(var)cout<<__LINE__<<' '<<#var<<"="<<var<<endl;
template<class S, class T> ostream& operator <<(ostream &os, const pair<S, T> v){
os << "( " << v.first << ", " << v.second << ")"; return os;
}
template<class T> ostream& operator <<(ostream &os, const vector<T> &v){
for(int i = 0; i < v.size(); i++){if(i > 0){os << " ";} os << v[i];} return os;
}
template<class T> ostream& operator <<(ostream &os, const vector<vector<T>> &v){
for(int i = 0; i < v.size(); i++){if(i > 0){os << endl;} os << v[i];} return os;
}
template<class T> ostream& operator <<(ostream &os, const vector<set<T>> &v){
for(int i = 0; i < v.size(); i++){if(i > 0){os << endl;} os << v[i];} return os;
}
template<class T> ostream& operator <<(ostream &os, const set<T> &v){
int i=0;
for(auto it:v){
if(i > 0){os << ' ';}
os << it;
i++;
}
return os;
}
using ll=long long;
using ld = long double;
#include<vector>
const ll mod = 998244353;
ll mod_pow(ll a, ll n) {
ll res = 1;
while (n) {
if (n & 1)res = res * a%mod;
a = a * a%mod; n >>= 1;
}
return res;
}
ll mod_inverse(ll a) {
return mod_pow(a, mod - 2);
}
ll root[24], invroot[24];
void init() {
static bool flag=false;
if(!flag){
flag=true;
for(int i=0;i<24;++i) {
int n = (1 << i);
root[i] = mod_pow(3, (mod - 1) / n);
invroot[i] = mod_inverse(root[i]);
}
}
}
typedef vector <ll> poly;
poly dft(poly f, bool inverse = false) {
init();
int n = f.size(); int i, j, k;
//bit
for (i = 0, j = 1; j < n - 1; j++) {
for (k = n >> 1; k >(i ^= k); k >>= 1);
if (i > j)swap(f[i], f[j]);
}
for (int j = 1; (1 << j) <= n; j++) {
int m = 1 << j;
ll zeta = root[j];
if (inverse)zeta = invroot[j];
for (i = 0; i < n; i += m) {
ll powzeta = 1;
for (k = i; k < i + m / 2; k++) {
ll t1 = f[k], t2 = powzeta * f[k + m / 2] % mod;
f[k] = t1 + t2; while (f[k] >= mod)f[k] -= mod;
f[k + m / 2] = t1 - t2 + mod; while (f[k + m / 2] >= mod)f[k + m / 2] -= mod;
(powzeta *= zeta) %= mod;
}
}
}
if (inverse) {
ll rv = mod_inverse(n);
for (i = 0; i < n; i++) {
(f[i] *= rv) %= mod;
}
}
return f;
}
poly multiply(poly g, poly h) {
int n = 1;
int pi = 0, qi = 0;
for(int i=0;i<g.size();++i)if (g[i])pi = i;
for(int i=0;i<h.size();++i)if (h[i])qi = i;
int sz = pi + qi + 2;
while (n < sz)n *= 2;
g.resize(n); h.resize(n);
/*while (g.size() < n) {
g.push_back(0);
}
while (h.size() < n) {
h.push_back(0);
}*/
poly gg = dft(g);
poly hh = dft(h);
poly ff; ff.resize(n);
for(int i=0;i<n;++i){
ff[i] = gg[i] * hh[i] % mod;
}
return dft(ff, true);
}
int main() {
ios::sync_with_stdio(false);
cin.tie();
init();
int N,K;cin>>N>>K;
ll now=1;
vector<ll>p1(K+1);
// 1/1 32/2 243/6 1024/24 ...
for(int i=0;i<=K;++i){
p1[i]=mod_pow(i+1,N)*now%mod;
now=now*mod_pow(i+2,mod-2);
now%=mod;
}
vector<ll>p2(K+1);
// 1/1 1/(-1) 2/1 6/(-1) ...
now=1;
for(int i=0;i<=K;++i){
p2[i]=now;
now*=mod_pow(i+1,mod-2);
now%=mod;
now*=mod-1;
now%=mod;
}
//WHATS(p1)
// WHATS(p2)
auto p=multiply(p1,p2);
ll fac=1;
//WHATS(p)
for(int i=0;i<p.size();++i){
p[i]*=fac;
p[i]%=mod;
fac=fac*(i+2)%mod;
}
vector<ll>facts(max(N,K)+1);
vector<ll>invs(max(N,K)+1);
facts[0]=1;
facts[1]=1;
invs[0]=1;
invs[1]=1;
for(int i=2;i<=max(N,K);++i){
facts[i]=facts[i-1]*i%mod;
invs[i]=invs[i-1]*mod_pow(i,mod-2)%mod;
}
ll answer=0;
for(int i=1;i<=N;++i){
if(K>=i&&(K-i)%2==1){
answer+=p[i-1]*facts[K]%mod*invs[K-i]%mod*invs[i]%mod;
answer%=mod;
}
}
cout<<answer<<endl;
//WHATS(p)
return 0;
}
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