test/yukicoder/5011.test.cpp

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• Last update: 2021-03-25 09:46:10+09:00
• Problem: https://yukicoder.me/problems/5011

Depends on

• math/quotients.cpp
• mod/mint.cpp

Code

// verification-helper: PROBLEM https://yukicoder.me/problems/5011

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

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

signed main(){
  cin.tie(0);
  ios::sync_with_stdio(0);
  using ll = long long;

  ll n;
  cin>>n;

  using M = Mint<int>;
  M ans{0};

  for(auto[l,r]:quotients(n)){
    if(l==1) continue;

    ll d=n/l;
    if(d<l){
      ans+=M(n)*M(r-l+1);
      ans-=M(d)*M(l-1+r-1)*M(r-l+1)/M(2);
      continue;
    }

    for(ll i=l;i<=r;i++)
      for(ll t=n;t;t/=i) ans+=M(t%i);
  }

  cout<<ans<<endl;
  return 0;
}

#line 1 "test/yukicoder/5011.test.cpp"
// verification-helper: PROBLEM https://yukicoder.me/problems/5011

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

#define call_from_test
#line 1 "math/quotients.cpp"

#line 3 "math/quotients.cpp"
using namespace std;
#endif
//BEGIN CUT HERE
// split [1, n] into ranges whose elements have same quotients
template<typename T>
decltype(auto) quotients(T n){
  vector<pair<T, T>> vp;
  T m;
  for(m=1;m*m<=n;m++) vp.emplace_back(m,m);
  for(T i=m;i>=1;i--){
    T l=n/(i+1)+1,r=n/i;
    if(l<=r and vp.back().second<l)
      vp.emplace_back(l,r);
  }
  return vp;
}
//END CUT HERE
#ifndef call_from_test
//INSERT ABOVE HERE
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 9 "test/yukicoder/5011.test.cpp"
#undef call_from_test

signed main(){
  cin.tie(0);
  ios::sync_with_stdio(0);
  using ll = long long;

  ll n;
  cin>>n;

  using M = Mint<int>;
  M ans{0};

  for(auto[l,r]:quotients(n)){
    if(l==1) continue;

    ll d=n/l;
    if(d<l){
      ans+=M(n)*M(r-l+1);
      ans-=M(d)*M(l-1+r-1)*M(r-l+1)/M(2);
      continue;
    }

    for(ll i=l;i<=r;i++)
      for(ll t=n;t;t/=i) ans+=M(t%i);
  }

  cout<<ans<<endl;
  return 0;
}

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