結果

問題 No.125 悪の花弁
ユーザー koyumeishi
提出日時 2016-06-08 20:52:26
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 117 ms / 5,000 ms
コード長 5,089 bytes
コンパイル時間 1,107 ms
コンパイル使用メモリ 108,892 KB
実行使用メモリ 19,776 KB
最終ジャッジ日時 2024-10-11 05:10:21
合計ジャッジ時間 2,283 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge4
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ファイルパターン 結果
other AC * 6
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#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;
}
// nCk mod p, O(1)
// precomputation O(size)
class combination_mod{
  const long long mod;
  const long long size;
  
  vector<long long> fact; //n!
  vector<long long> fact_inv; // (n!)^-1
  void make_fact(){
    fact[0] = 1;
    for(long long i=1; i<size; i++){
      fact[i] = fact[i-1]*i % mod;
    }
  }
  void make_fact_inv(){
    fact_inv[0] = fact_inv[1] = 1;
    for(long long i=2; i<size; i++){
      fact_inv[i] = fact_inv[mod%i] * (mod - mod/i) % mod;  // x ^ -1
    }
    for(int i=2; i<size; i++){
      fact_inv[i] = fact_inv[i-1] * fact_inv[i] % mod;  // x! ^ -1
    }
  }
public:
  combination_mod(long long mod_, long long size_ = 2000000) : mod(mod_), size(size_+1){
    fact.resize(size);
    fact_inv.resize(size);
    make_fact();
    make_fact_inv();
  }
  //nCk mod p O(1)
  long long comb(long long n, long long k){
    if(k==0 || n==k) return 1;
    long long ret = fact[n] * fact_inv[k] % mod * fact_inv[n-k] % mod;
    return ret;
  }
};
long long totient(long long n){
  long long ret = n;
  for(long long p=2; p*p <= n; p++){
    if(n%p != 0) continue;
    while(n%p == 0){
      n /= p;
    }
    ret = ret - ret / p;
  }
  if(n != 1){
    ret = ret - ret / n;
  }
  return ret;
}
vector<long long> divisors(long long N){
  if(N==1) return {1LL};
  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;
}
int main(){
  long long k;
  cin >> k;
  vector<long long> c(k);
  cin >> c;
  long long sum = accumulate(c.begin(), c.end(), 0ll);
  combination_mod comb(mod, sum+1);
  long long ans = 0;
  long long g = c[0];
  for(auto v : c) g = gcd(g, v);
  auto d = divisors(g);
  
  for(auto v : d){
    long long tmp = 1;
    long long acc = 0;
    for(int i=0; i<k; i++){
      tmp *= comb.comb((sum - acc)/v, c[i]/v);
      tmp %= mod;
      acc += c[i];
    }
    tmp *= totient(v);
    tmp %= mod;
    ans += tmp;
    ans %= mod;
  }
  ans *= mod_inverse(sum, mod);
  ans %= mod;
  println(ans);
  return 0;
}
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