結果
問題 | No.1100 Boxes |
ユーザー |
![]() |
提出日時 | 2020-06-26 22:17:14 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 363 ms / 2,000 ms |
コード長 | 5,825 bytes |
コンパイル時間 | 3,371 ms |
コンパイル使用メモリ | 205,424 KB |
最終ジャッジ日時 | 2025-01-11 11:42:25 |
ジャッジサーバーID (参考情報) |
judge4 / judge3 |
(要ログイン)
ファイルパターン | 結果 |
---|---|
sample | AC * 4 |
other | AC * 36 |
ソースコード
#include <bits/stdc++.h>using namespace std;template<typename T1,typename T2> inline void chmin(T1 &a,T2 b){if(a>b) a=b;}template<typename T1,typename T2> inline void chmax(T1 &a,T2 b){if(a<b) a=b;}using Int = long long;const char newl = '\n';template<typename T,T MOD = 1000000007>struct Mint{static constexpr T mod = MOD;T v;Mint():v(0){}Mint(signed v):v(v){}Mint(long long t){v=t%MOD;if(v<0) v+=MOD;}Mint pow(long long k){Mint res(1),tmp(v);while(k){if(k&1) res*=tmp;tmp*=tmp;k>>=1;}return res;}static Mint add_identity(){return Mint(0);}static Mint mul_identity(){return Mint(1);}Mint inv(){return pow(MOD-2);}Mint& operator+=(Mint a){v+=a.v;if(v>=MOD)v-=MOD;return *this;}Mint& operator-=(Mint a){v+=MOD-a.v;if(v>=MOD)v-=MOD;return *this;}Mint& operator*=(Mint a){v=1LL*v*a.v%MOD;return *this;}Mint& operator/=(Mint a){return (*this)*=a.inv();}Mint operator+(Mint a) const{return Mint(v)+=a;}Mint operator-(Mint a) const{return Mint(v)-=a;}Mint operator*(Mint a) const{return Mint(v)*=a;}Mint operator/(Mint a) const{return Mint(v)/=a;}Mint operator-() const{return v?Mint(MOD-v):Mint(v);}bool operator==(const Mint a)const{return v==a.v;}bool operator!=(const Mint a)const{return v!=a.v;}bool operator <(const Mint a)const{return v <a.v;}static Mint comb(long long n,int k){Mint num(1),dom(1);for(int i=0;i<k;i++){num*=Mint(n-i);dom*=Mint(i+1);}return num/dom;}};template<typename T,T MOD> constexpr T Mint<T, MOD>::mod;template<typename T,T MOD>ostream& operator<<(ostream &os,Mint<T, MOD> m){os<<m.v;return os;}template<typename M_>class Enumeration{using M = M_;protected:static vector<M> fact,finv,invs;public:static void init(int n){n=min<decltype(M::mod)>(n,M::mod-1);int m=fact.size();if(n<m) return;fact.resize(n+1,1);finv.resize(n+1,1);invs.resize(n+1,1);if(m==0) m=1;for(int i=m;i<=n;i++) fact[i]=fact[i-1]*M(i);finv[n]=M(1)/fact[n];for(int i=n;i>=m;i--) finv[i-1]=finv[i]*M(i);for(int i=m;i<=n;i++) invs[i]=finv[i]*fact[i-1];}static M Fact(int n){init(n);return fact[n];}static M Finv(int n){init(n);return finv[n];}static M Invs(int n){init(n);return invs[n];}static M C(int n,int k){if(n<k||k<0) return M(0);init(n);return fact[n]*finv[n-k]*finv[k];}static M P(int n,int k){if(n<k||k<0) return M(0);init(n);return fact[n]*finv[n-k];}// put n identical balls into k distinct boxesstatic M H(int n,int k){if(n<0||k<0) return M(0);if(!n&&!k) return M(1);init(n+k);return C(n+k-1,n);}};template<typename M>vector<M> Enumeration<M>::fact=vector<M>();template<typename M>vector<M> Enumeration<M>::finv=vector<M>();template<typename M>vector<M> Enumeration<M>::invs=vector<M>();// put n distinct balls into k distinct boxestemplate<typename M>M surjection(int n,int k){using E = Enumeration<M>;E::init(k);M res(0);for(int i=1;i<=k;i++){M tmp=E::C(k,i)*M(i).pow(n);if((k-i)&1) res-=tmp;else res+=tmp;}return res;}constexpr int bmds(int x){const int v[] = {1012924417, 924844033, 998244353,897581057, 645922817};return v[x];}constexpr int brts(int x){const int v[] = {5, 5, 3, 3, 3};return v[x];}template<int X>struct NTT{static constexpr int md = bmds(X);static constexpr int rt = brts(X);using M = Mint<int, md>;vector< vector<M> > rts,rrts;void ensure_base(int n){if((int)rts.size()>=n) return;rts.resize(n);rrts.resize(n);for(int i=1;i<n;i<<=1){if(!rts[i].empty()) continue;M w=M(rt).pow((md-1)/(i<<1));M rw=w.inv();rts[i].resize(i);rrts[i].resize(i);rts[i][0]=M(1);rrts[i][0]=M(1);for(int k=1;k<i;k++){rts[i][k]=rts[i][k-1]*w;rrts[i][k]=rrts[i][k-1]*rw;}}}void ntt(vector<M> &as,bool f){int n=as.size();assert((n&(n-1))==0);ensure_base(n);for(int i=0,j=1;j+1<n;j++){for(int k=n>>1;k>(i^=k);k>>=1);if(i>j) swap(as[i],as[j]);}for(int i=1;i<n;i<<=1){for(int j=0;j<n;j+=i*2){for(int k=0;k<i;k++){M z=as[i+j+k]*(f?rrts[i][k]:rts[i][k]);as[i+j+k]=as[j+k]-z;as[j+k]+=z;}}}if(f){M tmp=M(n).inv();for(int i=0;i<n;i++) as[i]*=tmp;}}vector<M> multiply(vector<M> as,vector<M> bs){int need=as.size()+bs.size()-1;int sz=1;while(sz<need) sz<<=1;as.resize(sz,M(0));bs.resize(sz,M(0));ntt(as,0);ntt(bs,0);for(int i=0;i<sz;i++) as[i]*=bs[i];ntt(as,1);as.resize(need);return as;}vector<int> multiply(vector<int> as,vector<int> bs){vector<M> am(as.size()),bm(bs.size());for(int i=0;i<(int)am.size();i++) am[i]=M(as[i]);for(int i=0;i<(int)bm.size();i++) bm[i]=M(bs[i]);vector<M> cm=multiply(am,bm);vector<int> cs(cm.size());for(int i=0;i<(int)cs.size();i++) cs[i]=cm[i].v;return cs;}};template<int X> constexpr int NTT<X>::md;template<int X> constexpr int NTT<X>::rt;//INSERT ABOVE HEREsigned main(){cin.tie(0);ios::sync_with_stdio(0);NTT<2> ntt;using M = decltype(ntt)::M;using E = Enumeration<M>;int n,k;cin>>n>>k;E::init(n+k);vector<M> as(k+1),bs(k+1);for(int e=1;e<k;e+=2){int p=k-e;as[e]=(p%2==0?M(1):-M(1))*E::Finv(e);}for(int i=0;i<=k;i++) bs[i]=E::Finv(i);auto cs=ntt.multiply(as,bs);cs.resize(k+1);M ans{0};for(int i=0;i<=k;i++)ans+=cs[k-i]*M(i).pow(n)*(i%2==0?M(1):-M(1))*E::Finv(i);ans*=E::Fact(k);cout<<ans<<newl;return 0;}