結果
問題 | No.1100 Boxes |
ユーザー |
![]() |
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 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 4 |
other | AC * 36 |
ソースコード
#include <iostream>#include <algorithm>#include <iomanip>#include <vector>#include <queue>#include <set>#include <map>#define N_MAX 200002using namespace std;typedef long long ll;#define MOD 998244353#define root 3unsigned 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;}