test/yukicoder/0022.test.cpp

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Last update: 2021-03-25 09:46:10+09:00
Problem: https://yukicoder.me/problems/22

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// verification-helper: PROBLEM https://yukicoder.me/problems/22

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

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

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

  using M = Mint<int, int(1e9+9)>;
  const int MAX = 666 * 6 + 10;
  vector<M> dp(MAX,0);
  dp[0]=M(1);

  for(int x:{1,5,10,50,100,500})
    for(int j=x;j<MAX;j++) dp[j]+=dp[j-x];

  int T;
  cin>>T;
  while(T--){
    using ll = long long;
    ll m;
    cin>>m;
    vector<M> ys(6);
    for(int i=0;i<6;i++) ys[i]=dp[(m%500)+(i*500)];
    cout<<lagrange_interpolation(ys,M(m/500))<<"\n";
  }
  cout<<flush;
  return 0;
}

#line 1 "test/yukicoder/0022.test.cpp"
// verification-helper: PROBLEM https://yukicoder.me/problems/22

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

#define call_from_test
#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/lagrangeinterpolation.cpp"

#line 3 "polynomial/lagrangeinterpolation.cpp"
using namespace std;
#endif
//BEGIN CUT HERE
template<typename M>
M lagrange_interpolation(vector<M> &y,M t){
  int n=y.size()-1;
  if(t.v<=n) return y[t.v];

  vector<M> dp(n+1,1),pd(n+1,1);
  for(int i=0;i<n;i++) dp[i+1]=dp[i]*(t-M(i));
  for(int i=n;i>0;i--) pd[i-1]=pd[i]*(t-M(i));

  vector<M> fact(n+1,1),finv(n+1,1);
  for(int i=1;i<=n;i++) fact[i]=fact[i-1]*M(i);
  finv[n]=M(1)/fact[n];
  for(int i=n;i>=1;i--) finv[i-1]=finv[i]*M(i);

  M res(0);
  for(int i=0;i<=n;i++){
    M tmp=y[i]*dp[i]*pd[i]*finv[i]*finv[n-i];
    if((n-i)&1) res-=tmp;
    else res+=tmp;
  }
  return res;
}
//END CUT HERE
#ifndef call_from_test
signed main(){
  return 0;
}
#endif
#line 9 "test/yukicoder/0022.test.cpp"
#undef call_from_test

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

  using M = Mint<int, int(1e9+9)>;
  const int MAX = 666 * 6 + 10;
  vector<M> dp(MAX,0);
  dp[0]=M(1);

  for(int x:{1,5,10,50,100,500})
    for(int j=x;j<MAX;j++) dp[j]+=dp[j-x];

  int T;
  cin>>T;
  while(T--){
    using ll = long long;
    ll m;
    cin>>m;
    vector<M> ys(6);
    for(int i=0;i<6;i++) ys[i]=dp[(m%500)+(i*500)];
    cout<<lagrange_interpolation(ys,M(m/500))<<"\n";
  }
  cout<<flush;
  return 0;
}