#409482 (C++17) No.502 階乗を計算するだけ

• 問題: No.502 階乗を計算するだけ
• ユーザー: beet
• 提出日時: 2019-12-17 16:09:28
• 言語: C++17 (gcc 13.3.0 + boost 1.89.0)
• 結果: AC
• 実行時間: 847 ms / 1,000 ms
• コード長: 10,449 bytes
• コンパイル時間: 4,639 ms
• コンパイル使用メモリ: 237,052 KB
• 最終ジャッジ日時: 2025-01-08 11:54:45
• ジャッジサーバーID （参考情報）: judge2 / judge5

ファイルパターン	結果
other	AC * 52

ソースコード

#ifndef call_from_test
#include<bits/stdc++.h>
using namespace std;
#endif

#define call_from_test
#ifndef call_from_test
#include<bits/stdc++.h>
using namespace std;
#endif
//BEGIN CUT HERE
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;}
//END CUT HERE
#ifndef call_from_test

//INSERT ABOVE HERE
signed ABC127_E(){
  cin.tie(0);
  ios::sync_with_stdio(0);

  int h,w,k;
  cin>>h>>w>>k;
  using M = Mint<int>;

  M ans{0};
  for(int d=1;d<h;d++)
    ans+=M(d)*M(h-d)*M(w)*M(w);

  for(int d=1;d<w;d++)
    ans+=M(d)*M(w-d)*M(h)*M(h);

  ans*=M::comb(h*w-2,k-2);
  cout<<ans<<endl;
  return 0;
}
/*
  verified on 2019/06/12
  https://atcoder.jp/contests/abc127/tasks/abc127_e
*/

signed main(){
  //ABC127_E();
  return 0;
}
#endif

#ifndef call_from_test
#include<bits/stdc++.h>
using namespace std;

#define call_from_test
#include "../mod/mint.cpp"
#undef call_from_test

#endif
//BEGIN CUT HERE
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;
//END CUT HERE
#ifndef call_from_test
signed ATC001_C(){
  cin.tie(0);
  ios::sync_with_stdio(0);

  int n;
  cin>>n;
  vector<int> as(n+1,0),bs(n+1,0);
  for(int i=1;i<=n;i++) cin>>as[i]>>bs[i];

  NTT<0> ntt;
  auto cs=ntt.multiply(as,bs);
  for(int i=1;i<=n*2;i++) cout<<cs[i]<<"\n";
  cout<<flush;
  return 0;
}
/*
  verified on 2019/11/26
  https://atcoder.jp/contests/atc001/tasks/fft_c
*/

signed main(){
  ATC001_C();
  return 0;
}
#endif

#ifndef call_from_test
#include<bits/stdc++.h>
using namespace std;

#define call_from_test
#include "../mod/mint.cpp"
#include "numbertheoretictransform.cpp"
#undef call_from_test

#endif
//BEGIN CUT HERE
struct ArbitraryModConvolution{
  using ll = long long;
  static NTT<0> ntt0;
  static NTT<1> ntt1;
  static NTT<2> ntt2;

  static constexpr int pow(int a,int b,int md){
    int res=1;
    a=a%md;
    while(b){
      if(b&1) res=(ll)res*a%md;
      a=(ll)a*a%md;
      b>>=1;
    }
    return res;
  }

  static constexpr int inv(int x,int md){
    return pow(x,md-2,md);
  }

  inline void garner(int &c0,int c1,int c2,int m01,int MOD){
    static constexpr int r01=inv(ntt0.md,ntt1.md);
    static constexpr int r02=inv(ntt0.md,ntt2.md);
    static constexpr int r12=inv(ntt1.md,ntt2.md);

    c1=(ll)(c1-c0)*r01%ntt1.md;
    if(c1<0) c1+=ntt1.md;

    c2=(ll)(c2-c0)*r02%ntt2.md;
    c2=(ll)(c2-c1)*r12%ntt2.md;
    if(c2<0) c2+=ntt2.md;

    c0+=(ll)c1*ntt0.md%MOD;
    if(c0>=MOD) c0-=MOD;
    c0+=(ll)c2*m01%MOD;
    if(c0>=MOD) c0-=MOD;
  }

  inline void garner(vector< vector<int> > &cs,int MOD){
    int m01 =(ll)ntt0.md*ntt1.md%MOD;
    int sz=cs[0].size();
    for(int i=0;i<sz;i++) garner(cs[0][i],cs[1][i],cs[2][i],m01,MOD);
  }

  vector<int> multiply(vector<int> as,vector<int> bs,int MOD){
    vector< vector<int> > cs(3);
    cs[0]=ntt0.multiply(as,bs);
    cs[1]=ntt1.multiply(as,bs);
    cs[2]=ntt2.multiply(as,bs);
    size_t sz=as.size()+bs.size()-1;
    for(auto& v:cs) v.resize(sz);
    garner(cs,MOD);
    return cs[0];
  }

  template<typename T,T MOD>
  decltype(auto) multiply(vector< Mint<T, MOD> > am,
                          vector< Mint<T, MOD> > bm){
    using M = Mint<T, MOD>;
    vector<int> as(am.size()),bs(bm.size());
    for(int i=0;i<(int)as.size();i++) as[i]=am[i].v;
    for(int i=0;i<(int)bs.size();i++) bs[i]=bm[i].v;
    vector<int> cs=multiply(as,bs,MOD);
    vector<M> cm(cs.size());
    for(int i=0;i<(int)cm.size();i++) cm[i]=M(cs[i]);
    return cm;
  }
};
NTT<0> ArbitraryModConvolution::ntt0;
NTT<1> ArbitraryModConvolution::ntt1;
NTT<2> ArbitraryModConvolution::ntt2;
//END CUT HERE
#ifndef call_from_test

#define call_from_test
#include "../tools/fastio.cpp"
#include "../mod/enumeration.cpp"
#undef call_from_test

//INSERT ABOVE HERE
signed YUKI_829(){
  using ll = long long;
  int n,b;
  cin>>n>>b;
  vector<int> s(n);
  for(int i=0;i<n;i++) cin>>s[i];
  using M = Mint<int>;
  using E = Enumeration<M>;
  E::init(3e5);

  vector<int> cnt(n,0);
  for(int i=0;i<n;i++) cnt[s[i]]++;

  using P = pair<int, vector<int> > ;
  priority_queue<P> pq;
  pq.emplace(-1,vector<int>(1,1));

  int sum=0;
  for(int i=n-1;i>=0;i--){
    if(cnt[i]==0) continue;
    M x=E::H(sum,cnt[i]);
    M y=E::H(sum+1,cnt[i])-x;
    x*=E::Fact(cnt[i]);
    y*=E::Fact(cnt[i]);

    pq.emplace(-2,vector<int>({x.v,y.v}));
    sum+=cnt[i];
  }

  const int MOD = 1e9+7;
  ArbitraryModConvolution arb;
  while(pq.size()>1u){
    auto as=pq.top().second;pq.pop();
    auto bs=pq.top().second;pq.pop();
    auto cs=arb.multiply(as,bs,MOD);
    pq.emplace(-(int)cs.size(),cs);
  }

  auto dp=pq.top().second;
  M ans(0),res(1);
  for(int j=0;j<(int)dp.size();j++){
    ans+=M((ll)j*(ll)dp[j])*res;
    res*=M(b);
  }
  cout<<ans.v<<endl;
  return 0;
}
/*
  verified on 2019/09/08
  https://yukicoder.me/problems/no/829
*/

signed main(){
  YUKI_829();
  return 0;
}
#endif

#undef call_from_test

//BEGIN CUT HERE
int factorial(long long n,int MOD){
  if(n>=MOD) return 0;
  ArbitraryModConvolution arb;
  auto inv=[&](int a){return ArbitraryModConvolution::inv(a,MOD);};

  using ll = long long;
  auto add=[&](int a,int b){return a+b>=MOD?a+b-MOD:a+b;};
  auto sub=[&](int a,int b){return a-b<0?a-b+MOD:a-b;};
  auto mul=[&](int a,int b){return (ll)a*b%MOD;};
  auto div=[&](int a,int b){return mul(a,inv(b));};

  int d=1<<15;
  vector<int> fact(d*2+1,1),finv(d*2+1,1);
  for(int i=1;i<=d*2;i++) fact[i]=mul(fact[i-1],i);
  finv[d*2]=inv(fact[d*2]);
  for(int i=d*2-1;i>=0;i--) finv[i]=mul(finv[i+1],i+1);

  vector<int> seq({1,d+1});
  seq.reserve(d+1);

  int sz=1;
  while(sz<d){
    vector<int> aux(sz,1);
    vector<int> f(sz*4,0),g(sz*4,0);
    for(int i=0;i<=sz;i++){
      f[i]=mul(mul(finv[i],finv[sz-i]),seq[i]);
      if(((sz+i)&1)&&(f[i]!=0)) f[i]=MOD-f[i];
    }

    vector<int> pf(f);
    vector<int> as;
    as.emplace_back(sz+1);
    as.emplace_back(div(sz,d));
    as.emplace_back(add(div(sz,d),sz+1));

    for(int idx=0;idx<3;idx++){
      for(int i=0;i<sz*4;i++) f[i]=pf[i];
      for(int i=1;i<sz*2+2;i++)
        g[i]=inv(as[idx]+MOD-sz+i-1);
      f=arb.multiply(f,g,MOD);
      f.resize(sz*4);

      int prod=1;
      for(int i=0;i<=sz;i++) prod=mul(prod,sub(as[idx],i));

      for(int i=0;i<=sz;i++){
        f[sz+i+1]=mul(f[sz+i+1],prod);
        prod=mul(prod,add(as[idx],i+1));
        prod=div(prod,sub(as[idx],sz-i));
      }
      if(idx==0){
        for(int i=0;i<sz;i++)
          aux[i]=f[sz+i+1];
      }
      if(idx==1){
        for(int i=0;i<=sz;i++)
          seq[i]=mul(seq[i],f[sz+i+1]);
      }
      if(idx==2){
        for(int i=0;i<sz;i++)
          aux[i]=mul(aux[i],f[sz+i+1]);
      }
    }
    for(int x:aux) seq.emplace_back(x);
    sz<<=1;
  }

  int res=1;
  int l=min((ll)d,(n+1)/d);
  for(int i=0;i<l;i++) res=mul(res,seq[i]);
  for(int i=l*d+1;i<=n;i++) res=mul(res,i);
  return res;
}
//END CUT HERE
#ifndef call_from_test
//INSERT ABOVE HERE
signed YUKI_502(){
  const int MOD = 1e9+7;
  long long n;
  cin>>n;
  cout<<factorial(n,MOD)<<endl;
  return 0;
}
/*
  verified on 2019/12/17
  https://yukicoder.me/problems/no/502
*/

signed main(){
  YUKI_502();
  return 0;
}
#endif