結果

問題 No.1100 Boxes
ユーザー milanis48663220
提出日時 2020-09-20 01:58:04
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 63 ms / 2,000 ms
コード長 4,672 bytes
コンパイル時間 928 ms
コンパイル使用メモリ 91,080 KB
実行使用メモリ 12,436 KB
最終ジャッジ日時 2024-06-24 00:29:06
合計ジャッジ時間 3,195 ms
ジャッジサーバーID
(参考情報)
judge3 / 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 <iostream>
#include <algorithm>
#include <iomanip>
#include <vector>
#include <queue>
#include <set>
#include <map>
#define N_MAX 200002
using namespace std;
typedef long long ll;
#define MOD 998244353
#define root 3
unsigned int add(const unsigned int x, const unsigned int y){
return (x + y < MOD) ? x + y : x + y - MOD;
}
unsigned int sub(const unsigned int x, const unsigned int y){
return (x >= y) ? (x - y) : (MOD - y + x);
}
unsigned int mul(const unsigned int x, const unsigned int y){
return (unsigned long long)x * y % MOD;
}
unsigned int mod_pow(unsigned int x, unsigned int n){
unsigned int res = 1;
while(n > 0){
if(n & 1){ res = mul(res, x); }
x = mul(x, x);
n >>= 1;
}
return res;
}
unsigned int inverse(const unsigned int x){
return mod_pow(x, MOD - 2);
}
void ntt(vector<int>& a, const bool rev = false){
unsigned int i, j, k, l, p, q, r, s;
const unsigned int size = a.size();
if(size == 1) return;
vector<int> b(size);
r = rev ? (MOD - 1 - (MOD - 1) / size) : (MOD - 1) / size;
s = mod_pow(root, r);
vector<unsigned int> kp(size / 2 + 1, 1);
for(i = 0; i < size / 2; ++i) kp[i + 1] = mul(kp[i], s);
for(i = 1, l = size / 2; i < size; i <<= 1, l >>= 1){
for(j = 0, r = 0; j < l; ++j, r += i){
for(k = 0, s = kp[i * j]; k < i; ++k){
p = a[k + r], q = a[k + r + size / 2];
b[k + 2 * r] = add(p, q);
b[k + 2 * r + i] = mul(sub(p, q), s);
}
}
swap(a, b);
}
if(rev){
s = inverse(size);
for(i = 0; i < size; i++){ a[i] = mul(a[i], s); }
}
}
vector<int> convolute(const vector<int>& a, const vector<int>& b){
const int size = (int)a.size() + (int)b.size() - 1;
int t = 1;
while(t < size){ t <<= 1; }
vector<int> A(t, 0), B(t, 0);
for(int i = 0; i < (int)a.size(); i++){ A[i] = a[i]; }
for(int i = 0; i < (int)b.size(); i++){ B[i] = b[i]; }
ntt(A), ntt(B);
for (int i = 0; i < t; i++){ A[i] = mul(A[i], B[i]); }
ntt(A, true);
A.resize(size);
return A;
}
class ModInt{
public:
ll v;
ModInt(ll _v = 0){
v = _v;
}
ModInt operator+(ll n){
return ModInt((v+n)%MOD);
}
ModInt operator-(ll n){
return ModInt((v-n+MOD)%MOD);
}
ModInt operator*(ll n){
return ModInt((v*n)%MOD);
}
ModInt operator/(ll n){
return ModInt((ModInt(n).inv()*v).v%MOD);
}
void operator+=(ll n){
v = (v+n)%MOD;
}
void operator-=(ll n){
v = (v-n+MOD)%MOD;
}
void operator*=(ll n){
v = (v*n)%MOD;
}
ModInt operator+(ModInt n){
return ModInt((v+n.v)%MOD);
}
ModInt operator-(ModInt n){
return ModInt((v-n.v+MOD)%MOD);
}
ModInt operator*(ModInt n){
return ModInt((v*n.v)%MOD);
}
ModInt operator/(ModInt n){
return ModInt((n.inv()*v).v%MOD);
}
void operator+=(ModInt n){
v = (v+n.v)%MOD;
}
void operator-=(ModInt n){
v = (v-n.v+MOD)%MOD;
}
void operator*=(ModInt n){
v = (v*n.v)%MOD;
}
void operator=(ModInt n){
v = n.v;
}
void operator=(ll n){
v = n;
}
ModInt inv(){
if(v == 1) return ModInt(1);
else return ModInt(MOD-ModInt(MOD%v).inv().v*(MOD/v)%MOD);
}
};
ostream& operator<<(ostream& os, const ModInt& m){
os << m.v;
return os;
}
istream & operator >> (istream &in, ModInt &m){
in >> m.v;
return in;
}
ModInt pow(ModInt a, ll n) {
ModInt ans = 1;
ModInt tmp = a;
for (int i = 0; i <= 60; i++) {
ll m = (ll)1 << i;
if (m & n) {
ans *= tmp;
}
tmp *= tmp;
}
return ans;
}
ModInt inv[N_MAX],fac[N_MAX],finv[N_MAX];
void init(){
fac[0]=1;fac[1]=1;
finv[0]=1;finv[1]=1;
inv[1]=1;
for(int i=2;i<N_MAX;i++){
inv[i]=(ModInt)MOD-inv[MOD%i]*(MOD/i);
fac[i]=fac[i-1]*(ll) i;
finv[i]=finv[i-1]*inv[i];
}
}
int main(){
ios::sync_with_stdio(false);
cin.tie(0);
cout << setprecision(10) << fixed;
init();
ll N, K;
cin >> N >> K;
vector<int> a(K+1), b(K+1);
for(int i = 0; i <= K; i++){
int sgn = (i%2 == 0 ? 1 : -1);
a[i] = (finv[i]*sgn).v;
a[i] += MOD; a[i] %= MOD;
if(i%2 == 1) b[i] = finv[i].v;
// a[i] = 1; b[i] = 1;
}
auto c = convolute(a, b);
ModInt ans = 0;
for(int i = 0; i <= K; i++){
ModInt tmp = ModInt(c[i])*fac[K]*pow(K-i, N)*finv[K-i];
ans += tmp;
}
cout << ans << endl;
}
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