test/yukicoder/3211.test.cpp

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Last update: 2021-07-24 22:40:18+09:00
Problem: https://yukicoder.me/problems/3211

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// verification-helper: PROBLEM https://yukicoder.me/problems/3211

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

#define call_from_test
#include "../../vector/reversed.cpp"
#include "../../mod/mint.cpp"
#include "../../polynomial/berlekampmassey.cpp"
#undef call_from_test

signed main(){
  cin.tie(0);
  ios::sync_with_stdio(0);

  using M = Mint<int>;
  int p;
  cin>>p;

  const int n = 100;
  vector<M> as(n);
  as[0]=M(0);
  as[1]=M(0);
  as[2]=M(1);
  for(int i=3;i<n;i++) as[i]=M(p)*as[i-1]+as[i-2];

  vector<M> bs(n,M(0));
  for(int s=0;s<n;s++)
    for(int t=0;s+t<n;t++)
      bs[s+t]+=as[s]*as[t];

  auto cs=reversed(berlekamp_massey(bs));

  const int MAX = 2e6 + 100;
  vector<M> dp(MAX,0);
  for(int i=0;i<n;i++) dp[i]=bs[i];
  for(int i=n;i<MAX;i++)
    for(int j=0;j<(int)cs.size();j++)
      dp[i]-=dp[i-j]*cs[j];

  int q;
  cin>>q;
  for(int i=0;i<q;i++){
    int k;
    cin>>k;
    cout<<dp[k]<<"\n";
  }
  return 0;
}

#line 1 "test/yukicoder/3211.test.cpp"
// verification-helper: PROBLEM https://yukicoder.me/problems/3211

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

#define call_from_test
#line 1 "vector/reversed.cpp"

#line 3 "vector/reversed.cpp"
using namespace std;
#endif

//BEGIN CUT HERE
template<typename T>
vector<T> reversed(vector<T> vs){
  reverse(vs.begin(),vs.end());
  return vs;
}
//END CUT HERE
#ifndef call_from_test
signed main(){
  return 0;
}
#endif
#line 1 "mod/mint.cpp"

#line 3 "mod/mint.cpp"
using namespace std;
#endif

//BEGIN CUT HERE
template<typename T, T MOD = 1000000007>
struct Mint{
  inline 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 *this;}
  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;}

  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>
ostream& operator<<(ostream &os,Mint<T, MOD> m){os<<m.v;return os;}
//END CUT HERE
#ifndef call_from_test
signed main(){
  return 0;
}
#endif
#line 1 "polynomial/berlekampmassey.cpp"

#line 3 "polynomial/berlekampmassey.cpp"
using namespace std;
#endif
//BEGIN CUT HERE
// construct a charasteristic equation from sequence
// return a monic polynomial in O(n^2)
template<typename T>
vector<T> berlekamp_massey(vector<T> &as){
  using Poly = vector<T>;
  int n=as.size();
  Poly bs({-T(1)}),cs({-T(1)});
  T y(1);
  for(int ed=1;ed<=n;ed++){
    int l=cs.size(),m=bs.size();
    T x(0);
    for(int i=0;i<l;i++) x+=cs[i]*as[ed-l+i];
    bs.emplace_back(0);
    m++;
    if(x==T(0)) continue;
    T freq=x/y;
    if(m<=l){
      for(int i=0;i<m;i++)
        cs[l-1-i]-=freq*bs[m-1-i];
      continue;
    }
    auto ts=cs;
    cs.insert(cs.begin(),m-l,T(0));
    for(int i=0;i<m;i++) cs[m-1-i]-=freq*bs[m-1-i];
    bs=ts;
    y=x;
  }
  for(auto &c:cs) c/=cs.back();
  return cs;
}
//END CUT HERE
#ifndef call_from_test
signed main(){
  return 0;
}
#endif
#line 10 "test/yukicoder/3211.test.cpp"
#undef call_from_test

signed main(){
  cin.tie(0);
  ios::sync_with_stdio(0);

  using M = Mint<int>;
  int p;
  cin>>p;

  const int n = 100;
  vector<M> as(n);
  as[0]=M(0);
  as[1]=M(0);
  as[2]=M(1);
  for(int i=3;i<n;i++) as[i]=M(p)*as[i-1]+as[i-2];

  vector<M> bs(n,M(0));
  for(int s=0;s<n;s++)
    for(int t=0;s+t<n;t++)
      bs[s+t]+=as[s]*as[t];

  auto cs=reversed(berlekamp_massey(bs));

  const int MAX = 2e6 + 100;
  vector<M> dp(MAX,0);
  for(int i=0;i<n;i++) dp[i]=bs[i];
  for(int i=n;i<MAX;i++)
    for(int j=0;j<(int)cs.size();j++)
      dp[i]-=dp[i-j]*cs[j];

  int q;
  cin>>q;
  for(int i=0;i<q;i++){
    int k;
    cin>>k;
    cout<<dp[k]<<"\n";
  }
  return 0;
}