#430566 (C++17) No.8046 yukicoderの過去問

• 問題: No.8046 yukicoderの過去問
• ユーザー: beet
• 提出日時: 2020-02-15 01:24:25
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 161 ms / 2,000 ms
• コード長: 13,138 bytes
• コンパイル時間: 2,958 ms
• コンパイル使用メモリ: 214,620 KB
• 最終ジャッジ日時: 2025-01-09 00:38:35
• ジャッジサーバーID （参考情報）: judge1 / judge5

ファイルパターン	結果
other	AC * 9

ソースコード

#define PROBLEM "https://yukicoder.me/problems/2744"

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

#define call_from_test
#ifndef call_from_test
#include<bits/stdc++.h>
using namespace std;
#endif
//BEGIN CUT HERE
struct FastIO{
  FastIO(){
    cin.tie(0);
    ios::sync_with_stdio(0);
  }
}fastio_beet;
//END CUT HERE
#ifndef call_from_test
signed main(){
  return 0;
}
#endif

#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;
#endif
//BEGIN CUT HERE
namespace FFT{
  using dbl = double;

  struct num{
    dbl x,y;
    num(){x=y=0;}
    num(dbl x,dbl y):x(x),y(y){}
  };

  inline num operator+(num a,num b){
    return num(a.x+b.x,a.y+b.y);
  }
  inline num operator-(num a,num b){
    return num(a.x-b.x,a.y-b.y);
  }
  inline num operator*(num a,num b){
    return num(a.x*b.x-a.y*b.y,a.x*b.y+a.y*b.x);
  }
  inline num conj(num a){
    return num(a.x,-a.y);
  }

  int base=1;
  vector<num> rts={{0,0},{1,0}};
  vector<int> rev={0,1};

  const dbl PI=asinl(1)*2;

  void ensure_base(int nbase){
    if(nbase<=base) return;

    rev.resize(1<<nbase);
    for(int i=0;i<(1<<nbase);i++)
      rev[i]=(rev[i>>1]>>1)+((i&1)<<(nbase-1));

    rts.resize(1<<nbase);
    while(base<nbase){
      dbl angle=2*PI/(1<<(base+1));
      for(int i=1<<(base-1);i<(1<<base);i++){
        rts[i<<1]=rts[i];
        dbl angle_i=angle*(2*i+1-(1<<base));
        rts[(i<<1)+1]=num(cos(angle_i),sin(angle_i));
      }
      base++;
    }
  }

  void fft(vector<num> &as){
    int n=as.size();
    assert((n&(n-1))==0);

    int zeros=__builtin_ctz(n);
    ensure_base(zeros);
    int shift=base-zeros;
    for(int i=0;i<n;i++)
      if(i<(rev[i]>>shift))
        swap(as[i],as[rev[i]>>shift]);

    for(int k=1;k<n;k<<=1){
      for(int i=0;i<n;i+=2*k){
        for(int j=0;j<k;j++){
          num z=as[i+j+k]*rts[j+k];
          as[i+j+k]=as[i+j]-z;
          as[i+j]=as[i+j]+z;
        }
      }
    }
  }

  template<typename T>
  vector<long long> multiply(vector<T> &as,vector<T> &bs){
    int need=as.size()+bs.size()-1;
    int nbase=0;
    while((1<<nbase)<need) nbase++;
    ensure_base(nbase);

    int sz=1<<nbase;
    vector<num> fa(sz);
    for(int i=0;i<sz;i++){
      T x=(i<(int)as.size()?as[i]:0);
      T y=(i<(int)bs.size()?bs[i]:0);
      fa[i]=num(x,y);
    }
    fft(fa);

    num r(0,-0.25/sz);
    for(int i=0;i<=(sz>>1);i++){
      int j=(sz-i)&(sz-1);
      num z=(fa[j]*fa[j]-conj(fa[i]*fa[i]))*r;
      if(i!=j)
        fa[j]=(fa[i]*fa[i]-conj(fa[j]*fa[j]))*r;
      fa[i]=z;
    }
    fft(fa);

    vector<long long> res(need);
    for(int i=0;i<need;i++)
      res[i]=round(fa[i].x);

    return res;
  }

};
//END CUT HERE
#ifndef call_from_test
signed main(){
  return 0;
}
#endif

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

#define call_from_test
#include "fastfouriertransform.cpp"
#undef call_from_test

#endif
//BEGIN CUT HERE
template<typename T>
struct ArbitraryMod{
  using dbl=FFT::dbl;
  using num=FFT::num;

  vector<T> multiply(vector<T> as,vector<T> bs){
    int need=as.size()+bs.size()-1;
    int sz=1;
    while(sz<need) sz<<=1;
    vector<num> fa(sz),fb(sz);
    for(int i=0;i<(int)as.size();i++)
      fa[i]=num(as[i].v&((1<<15)-1),as[i].v>>15);
    for(int i=0;i<(int)bs.size();i++)
      fb[i]=num(bs[i].v&((1<<15)-1),bs[i].v>>15);

    fft(fa);fft(fb);

    dbl ratio=0.25/sz;
    num r2(0,-1),r3(ratio,0),r4(0,-ratio),r5(0,1);
    for(int i=0;i<=(sz>>1);i++){
      int j=(sz-i)&(sz-1);
      num a1=(fa[i]+conj(fa[j]));
      num a2=(fa[i]-conj(fa[j]))*r2;
      num b1=(fb[i]+conj(fb[j]))*r3;
      num b2=(fb[i]-conj(fb[j]))*r4;
      if(i!=j){
        num c1=(fa[j]+conj(fa[i]));
        num c2=(fa[j]-conj(fa[i]))*r2;
        num d1=(fb[j]+conj(fb[i]))*r3;
        num d2=(fb[j]-conj(fb[i]))*r4;
        fa[i]=c1*d1+c2*d2*r5;
        fb[i]=c1*d2+c2*d1;
      }
      fa[j]=a1*b1+a2*b2*r5;
      fb[j]=a1*b2+a2*b1;
    }
    fft(fa);fft(fb);

    vector<T> cs(need);
    using ll = long long;
    for(int i=0;i<need;i++){
      ll aa=T(llround(fa[i].x)).v;
      ll bb=T(llround(fb[i].x)).v;
      ll cc=T(llround(fa[i].y)).v;
      cs[i]=T(aa+(bb<<15)+(cc<<30));
    }
    return cs;
  }
};
//END CUT HERE
#ifndef call_from_test
signed main(){
  return 0;
}
#endif

#ifndef call_from_test
#include<bits/stdc++.h>
using namespace std;
#endif
//BEGIN CUT HERE
template<typename T>
struct FormalPowerSeries{
  using Poly = vector<T>;
  using Conv = function<Poly(Poly, Poly)>;
  Conv conv;
  FormalPowerSeries(Conv conv):conv(conv){}

  Poly pre(const Poly &as,int deg){
    return Poly(as.begin(),as.begin()+min((int)as.size(),deg));
  }

  Poly add(Poly as,Poly bs){
    int sz=max(as.size(),bs.size());
    Poly cs(sz,T(0));
    for(int i=0;i<(int)as.size();i++) cs[i]+=as[i];
    for(int i=0;i<(int)bs.size();i++) cs[i]+=bs[i];
    return cs;
  }

  Poly sub(Poly as,Poly bs){
    int sz=max(as.size(),bs.size());
    Poly cs(sz,T(0));
    for(int i=0;i<(int)as.size();i++) cs[i]+=as[i];
    for(int i=0;i<(int)bs.size();i++) cs[i]-=bs[i];
    return cs;
  }

  Poly mul(Poly as,Poly bs){
    return conv(as,bs);
  }

  Poly mul(Poly as,T k){
    for(auto &a:as) a*=k;
    return as;
  }

  // F(0) must not be 0
  Poly inv(Poly as,int deg){
    assert(as[0]!=T(0));
    Poly rs({T(1)/as[0]});
    for(int i=1;i<deg;i<<=1)
      rs=pre(sub(add(rs,rs),mul(mul(rs,rs),pre(as,i<<1))),i<<1);
    return rs;
  }

  // not zero
  Poly div(Poly as,Poly bs){
    while(as.back()==T(0)) as.pop_back();
    while(bs.back()==T(0)) bs.pop_back();
    if(bs.size()>as.size()) return Poly();
    reverse(as.begin(),as.end());
    reverse(bs.begin(),bs.end());
    int need=as.size()-bs.size()+1;
    Poly ds=pre(mul(as,inv(bs,need)),need);
    reverse(ds.begin(),ds.end());
    return ds;
  }

  Poly mod(Poly as,Poly bs){
    if(as==Poly(as.size(),0)) return Poly({0});
    as=sub(as,mul(div(as,bs),bs));
    if(as==Poly(as.size(),0)) return Poly({0});
    while(as.back()==T(0)) as.pop_back();
    return as;
  }

  // F(0) must be 1
  Poly sqrt(Poly as,int deg){
    assert(as[0]==T(1));
    T inv2=T(1)/T(2);
    Poly ss({T(1)});
    for(int i=1;i<deg;i<<=1){
      ss=pre(add(ss,mul(pre(as,i<<1),inv(ss,i<<1))),i<<1);
      for(T &x:ss) x*=inv2;
    }
    return ss;
  }

  Poly diff(Poly as){
    int n=as.size();
    Poly rs(n-1);
    for(int i=1;i<n;i++) rs[i-1]=as[i]*T(i);
    return rs;
  }

  Poly integral(Poly as){
    int n=as.size();
    Poly rs(n+1);
    rs[0]=T(0);
    for(int i=0;i<n;i++) rs[i+1]=as[i]/T(i+1);
    return rs;
  }

  // F(0) must be 1
  Poly log(Poly as,int deg){
    return pre(integral(mul(diff(as),inv(as,deg))),deg);
  }

  // F(0) must be 0
  Poly exp(Poly as,int deg){
    Poly f({T(1)});
    as[0]+=T(1);
    for(int i=1;i<deg;i<<=1)
      f=pre(mul(f,sub(pre(as,i<<1),log(f,i<<1))),i<<1);
    return f;
  }

  Poly partition(int n){
    Poly rs(n+1);
    rs[0]=T(1);
    for(int k=1;k<=n;k++){
      if(1LL*k*(3*k+1)/2<=n) rs[k*(3*k+1)/2]+=T(k%2?-1LL:1LL);
      if(1LL*k*(3*k-1)/2<=n) rs[k*(3*k-1)/2]+=T(k%2?-1LL:1LL);
    }
    return inv(rs,n+1);
  }

  Poly bernoulli(int n){
    Poly rs(n+1,1);
    for(int i=1;i<=n;i++) rs[i]=rs[i-1]/T(i+1);
    rs=inv(rs,n+1);
    T tmp(1);
    for(int i=1;i<=n;i++){
      tmp*=T(i);
      rs[i]*=tmp;
    }
    return rs;
  }
};
//END CUT HERE
#ifndef call_from_test

#define call_from_test
#include "../mod/mint.cpp"
#include "../convolution/numbertheoretictransform.cpp"
#include "../mod/sqrt.cpp"
#include "../tools/fastio.cpp"
#undef call_from_test

//INSERT ABOVE HERE

signed HAPPYQUERY_E(){
  int n,m,q;
  cin>>n>>m>>q;
  vector<int> ls(q),rs(q);
  for(int i=0;i<q;i++) cin>>ls[i]>>rs[i],ls[i]--;

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

  if(as==vector<int>(n,0)){
    for(int i=0;i<m;i++){
      if(i) cout<<" ";
      cout<<0;
    }
    cout<<endl;
    return 0;
  }

  vector<int> cs(n-m+1,0);
  for(int l:ls) cs[l]++;

  NTT<0> ntt;
  using M = NTT<0>::M;
  auto conv=[&](auto as,auto bs){return ntt.multiply(as,bs);};
  FormalPowerSeries<M> FPS(conv);

  vector<M> ps(as.size()),qs(cs.size());
  for(int i=0;i<(int)ps.size();i++) ps[i]=M(as[i]);
  for(int i=0;i<(int)qs.size();i++) qs[i]=M(cs[i]);

  auto bs=FPS.div(ps,qs);
  for(int i=0;i<m;i++){
    if(i) cout<<" ";
    cout<<bs[i];
  }
  cout<<endl;
  return 0;
}
/*
  verified on 2019/09/17
  https://www.hackerrank.com/contests/happy-query-contest/challenges/array-restoring
*/

signed CFR250_E(){
  int n,m;
  cin>>n>>m;
  vector<int> cs(n);
  for(int i=0;i<n;i++) cin>>cs[i];

  NTT<2> ntt;
  using M = NTT<2>::M;
  auto conv=[&](auto as,auto bs){return ntt.multiply(as,bs);};
  FormalPowerSeries<M> FPS(conv);

  const int deg=1<<18;
  vector<M> as(deg,0);
  as[0]=M(1);
  for(int c:cs) as[c]-=M(4);

  auto bs=FPS.sqrt(as,deg);
  bs[0]+=M(1);

  vector<M> vs({2});

  auto ans=FPS.mul(vs,FPS.inv(bs,deg));
  for(int i=1;i<=m;i++) cout<<ans[i]<<"\n";
  cout<<flush;

  return 0;
}
/*
  verified on 2019/09/17
  https://codeforces.com/contest/438/problem/E
*/

signed LOJ_150(){
  NTT<2> ntt;
  using M = NTT<2>::M;
  auto conv=[&](auto as,auto bs){return ntt.multiply(as,bs);};
  FormalPowerSeries<M> FPS(conv);

  int n,k;
  cin>>n>>k;

  vector<M> F(n+1);
  for(int i=0;i<=n;i++) cin>>F[i].v;

  const int deg = 1<<17;
  auto as=FPS.log(FPS.mul(F,F[0].inv()),deg);
  auto bs=FPS.exp(FPS.mul(as,M((ntt.md-1)/2)),deg);
  M s(mod_sqrt(F[0].v,ntt.md)[0]);
  auto cs=FPS.integral(FPS.mul(bs,s.inv()));
  auto ds=FPS.exp(cs,deg);
  auto es=FPS.sub(F,ds);
  es[0]+=M(2);
  es[0]-=F[0];
  auto fs=FPS.log(es,deg);
  fs[0]+=M(1);
  auto gs=FPS.log(fs,deg);
  auto hs=FPS.mul(gs,M(k));
  auto is=FPS.exp(hs,deg);
  auto G=FPS.diff(is);

  for(int i=0;i<n;i++){
    if(i) cout<<" ";
    cout<<G[i];
  }
  cout<<endl;
  return 0;
}
/*
  verified on 2019/09/17
  https://loj.ac/problem/150
*/

signed CODECHEF_PSUM(){
  NTT<2> ntt;
  using M = NTT<2>::M;
  auto conv=[&](auto as,auto bs){return ntt.multiply(as,bs);};
  FormalPowerSeries<M> FPS(conv);

  int n,s,k;
  cin>>n>>s>>k;
  vector<int> cs(n),vs(n);
  for(int i=0;i<n;i++) cin>>cs[i]>>vs[i];

  const int deg = 1<<11;
  vector< vector<M> > dp(s+1,vector<M>(deg,0));
  dp[0][0]=M(1);

  auto nx=dp;
  for(int i=0;i<n;i++){
    auto ps=FPS.exp(vector<M>({M(0),M(vs[i])}),deg);
    for(int j=0;j+cs[i]<=s;j++){
      auto rs=FPS.mul(ps,dp[j]);
      for(int l=0;l<deg;l++) nx[j+cs[i]][l]+=rs[l];
    }
    dp=nx;
  }

  M ans{0};
  for(int i=1;i<=s;i++) ans+=dp[i][k];
  for(int i=1;i<=k;i++) ans*=M(i);
  cout<<ans<<endl;
  return 0;
}
/*
  verified on 2019/09/24
  https://www.codechef.com/problems/PSUM
*/

signed main(){
  //HAPPYQUERY_E();
  //CFR250_E();
  //LOJ_150();
  //CODECHEF_PSUM();
  return 0;
}
#endif

#undef call_from_test

signed main(){
  int k,n;
  cin>>k>>n;
  vector<int> xs(n);
  for(int i=0;i<n;i++) cin>>xs[i];

  using M = Mint<int>;
  ArbitraryMod<M> arb;
  auto conv=[&](auto as,auto bs){return arb.multiply(as,bs);};
  FormalPowerSeries<M> FPS(conv);

  const int sz=1<<17;
  vector<M> bs(sz,M(0));
  bs[0]=1;
  for(int x:xs) bs[x]-=M(1);
  cout<<FPS.inv(bs,k+1)[k]<<endl;
  return 0;
}