#96963 (C++14) No.377 背景パターン

• 問題: No.377 背景パターン
• ユーザー: koyumeishi
• 提出日時: 2016-06-08 17:49:46
• 言語: C++14 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 2,902 ms / 5,000 ms
• コード長: 7,160 bytes
• コンパイル時間: 1,502 ms
• コンパイル使用メモリ: 121,524 KB
• 実行使用メモリ: 21,164 KB
• 最終ジャッジ日時: 2024-10-11 01:12:18
• 合計ジャッジ時間: 5,975 ms
• ジャッジサーバーID （参考情報）: judge2 / judge3

ファイルパターン	結果
sample	AC * 5
other	AC * 14

ソースコード

#include <iostream>
#include <vector>
#include <cstdio>
#include <sstream>
#include <map>
#include <string>
#include <algorithm>
#include <queue>
#include <cmath>
#include <functional>
#include <set>
#include <ctime>
#include <random>
#include <chrono>
#include <cassert>
using namespace std;

namespace {
  using Integer = long long; //__int128;
  template<class T> istream& operator >> (istream& is, vector<T>& vec){for(T& val: vec) is >> val; return is;}
  template<class T> istream& operator ,  (istream& is, T& val){ return is >> val;}
  template<class T> ostream& operator << (ostream& os, const vector<T>& vec){for(int i=0; i<vec.size(); i++) os << vec[i] << (i==vec.size()-1?"":" "); return os;}
  template<class T> ostream& operator ,  (ostream& os, const T& val){ return os << " " << val;}

  template<class H> void print(const H& head){ cout << head; }
  template<class H, class ... T> void print(const H& head, const T& ... tail){ cout << head << " "; print(tail...); }
  template<class ... T> void println(const T& ... values){ print(values...); cout << endl; }

  template<class H> void eprint(const H& head){ cerr << head; }
  template<class H, class ... T> void eprint(const H& head, const T& ... tail){ cerr << head << " "; eprint(tail...); }
  template<class ... T> void eprintln(const T& ... values){ eprint(values...); cerr << endl; }

  string operator "" _s (const char* str, size_t size){ return move(string(str)); }
  constexpr Integer my_pow(Integer x, Integer k, Integer z=1){return k==0 ? z : k==1 ? z*x : (k&1) ? my_pow(x*x,k>>1,z*x) : my_pow(x*x,k>>1,z);}
  constexpr Integer my_pow_mod(Integer x, Integer k, Integer M, Integer z=1){return k==0 ? z%M : k==1 ? z*x%M : (k&1) ? my_pow_mod(x*x%M,k>>1,M,z*x%M) : my_pow_mod(x*x%M,k>>1,M,z);}
  constexpr unsigned long long operator "" _ten (unsigned long long value){ return my_pow(10,value); }

  inline int k_bit(Integer x, int k){return (x>>k)&1;} //0-indexed

  mt19937 mt(chrono::duration_cast<chrono::nanoseconds>(chrono::steady_clock::now().time_since_epoch()).count());

  template<class T> string join(const vector<T>& v, const string& sep){
    stringstream ss; for(int i=0; i<v.size(); i++){ if(i>0) ss << sep; ss << v[i]; } return ss.str();
  }
}

constexpr long long mod = 9_ten + 7;

long long gcd(long long a, long long b){ return (b==0)?a:gcd(b,a%b); }
template<class ... T> long long gcd(long long a, long long b, T ... c){ return gcd(gcd(a,b), c...);}
long long lcm(long long a, long long b){ if(a<b) swap(a,b); return (b==1)?a:a*(b/gcd(a,b)); }
template<class ... T> long long lcm(long long a, long long b, T ... c){ return lcm(lcm(a,b), c...);}


long long extgcd(long long a, long long b, long long &x, long long &y){
  long long d=a;
  if(b!=0){
    d = extgcd(b, a%b, y, x);
    y -= (a/b) * x;
  }else{
    x = 1;
    y = 0;
  }
  return d;
}

long long mod_inverse(long long a, long long m){
  long long x,y;
  extgcd(a,m,x,y);
  return (m+x%m)%m;
}


vector<long long> divisors(long long N){
  vector<long long> ret;
  ret.push_back(1);
  ret.push_back(N);

  for(long long i=2; i*i<=N; i++){
    if(N%i==0){
      ret.push_back(i);
      if(i*i != N) ret.push_back(N/i);
    }
  }

  sort(ret.begin(), ret.end());
  return ret;
}

namespace Montgomery{
  template<long long MOD>
  constexpr long long PRE_COMP(long long r, long long res=0, long long t=0, long long i = 1){
    return (r>1) ? ( PRE_COMP<MOD>(r/2, res + (t%2==0?i:0), (t%2==0?(t+MOD):t) / 2, i*2) ):( res );
  }

  template<long long MOD>
  class Values{
  public:
    static constexpr long long R = 1LL<<30; // R>MOD && gcd(R,MOD)==1
    static constexpr long long mask = (1LL<<30)-1;
    static constexpr long long R2 = (R*R)%MOD;
    static constexpr long long Ninv = PRE_COMP<MOD>(1<<30); // N*Ninv = R-1 mod R
    static long long Reduction(long long x){
      long long s = ((x & mask) * Ninv) & mask;
      long long ret = (x + s*MOD ) >> 30;
      if(ret>=MOD) ret -= MOD;
      return ret;
    }
  };

  template<long long MOD> struct M_Int{
    long long value;
    M_Int() : value(0) {}
    M_Int(long long val, bool convert=true) : value(convert ? Values<MOD>::Reduction(val * Values<MOD>::R2) : val){} //convert==true : int -> M_Int, false : M_Int::value -> M_Int
    M_Int(const M_Int& x) : value( x.value ){} //M_Int -> M_Int
    M_Int& operator = (const M_Int& x){ value = x.value; return *this; }
    M_Int& operator = (const long long& x){ value = Values<MOD>::Reduction(x * Values<MOD>::R2); return *this; }

    M_Int operator * (const M_Int& x)    { return M_Int( Values<MOD>::Reduction(value * x.value) , false ); }
    M_Int operator * (const long long& x){ return (*this) * M_Int(x); }
    template<class T> M_Int& operator *= (const T& x){ return (*this) = (*this)*x; }

    M_Int operator + (const M_Int& x)    { long long tmp = value + x.value; if(tmp >= MOD) tmp -= MOD; return M_Int(tmp, false); }
    M_Int operator + (const long long& x){ return (*this)+M_Int(x); }
    template<class T> M_Int& operator += (const T& x)    { return (*this) = (*this) + x; }

    M_Int operator - (const M_Int& x)    { long long tmp = value - x.value; if(tmp < 0  ) tmp += MOD; return M_Int(tmp, false); }
    M_Int operator - (const long long& x){ return (*this)-M_Int(x); }
    template<class T> M_Int& operator -= (const T& x)    { return (*this) = (*this) - x; }

    bool operator == (const M_Int& x){ return value == x.value; }
    bool operator == (const long long& x){ M_Int tmp(x); return (*this)==tmp; }
    long long to_i () { // M_int -> int
      return Values<MOD>::Reduction(value);
    }
    operator long long () { // M_int -> int
      return Values<MOD>::Reduction(value);
    }
  };

  template<long long MOD> istream& operator>>(istream& is, M_Int<MOD>& v){ long long tmp; is >> tmp; v=tmp; return is; }
  template<long long MOD> ostream& operator<<(ostream& os, M_Int<MOD> v){ return os << v.to_i(); }

  template<long long MOD> M_Int<MOD> operator + (long long l, M_Int<MOD> r){ return r+l; }
  template<long long MOD> M_Int<MOD> operator - (long long l, M_Int<MOD> r){ return r-l; }
  template<long long MOD> M_Int<MOD> operator * (long long l, M_Int<MOD> r){ return r*l; }
}

using mint =  Montgomery::M_Int<1000000007>;

mint mint_pow(mint x, long long y){  //x^y
  if(x.to_i()==0 && y!=0) return 0;
  mint ret=1LL;
  while(y){
    if(y&1LL) ret *= x;
    x *= x;
    y >>= 1LL;
  }
  return ret;
}

int main(){
  long long h,w,k;
  cin >> h,w,k;
  mint ans = 0;
  map<long long, mint> res;

  long long l = lcm(h,w);
  
  auto v1 = divisors(h);
  auto v2 = divisors(w);
  vector<long long> v;
  for(auto x : v1){
    for(auto y : v2){
      if(x*y > l) break;
      v.push_back( x * y );
    }
  }
  sort(v.begin(), v.end());
  v.erase( unique(v.begin(), v.end()), v.end());

  for(auto d : v){
    mint tmp = mint(gcd(h,d)) * mint(gcd(w,d));
    for(auto dd : v){
      if(dd*dd > d) break;
      if(d%dd == 0){
        tmp -= res[dd];
        if(dd*dd != d){
          tmp -= res[d/dd];
        }
      }
    }
    res[d] = tmp;

    ans += mint_pow(k, h*w/d) * tmp;
  }

  ans *= mint( mod_inverse(h*w, mod) );

  println(ans.to_i());

  return 0;
}