結果

問題 No.125 悪の花弁
コンテスト
ユーザー fumiphys
提出日時 2019-09-12 22:42:26
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
WA  
実行時間 -
コード長 5,842 bytes
コンパイル時間 1,839 ms
コンパイル使用メモリ 179,536 KB
実行使用メモリ 19,320 KB
最終ジャッジ日時 2024-07-02 17:12:38
合計ジャッジ時間 2,918 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge2
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ファイルパターン 結果
other AC * 2 WA * 4
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ソースコード

diff # 

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

// macros
#define pb emplace_back
#define mk make_pair
#define FOR(i, a, b) for(int i=(a);i<(b);++i)
#define rep(i, n) FOR(i, 0, n)
#define rrep(i, n) for(int i=((int)(n)-1);i>=0;i--)
#define irep(itr, st) for(auto itr = (st).begin(); itr != (st).end(); ++itr)
#define irrep(itr, st) for(auto itr = (st).rbegin(); itr != (st).rend(); ++itr)
#define all(x) (x).begin(),(x).end()
#define sz(x) ((int)(x).size())
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end())
#define bit(n) (1LL<<(n))
// functions
template <class T>bool chmax(T &a, const T &b){if(a < b){a = b; return 1;} return 0;}
template <class T>bool chmin(T &a, const T &b){if(a > b){a = b; return 1;} return 0;}
template <typename T> istream &operator>>(istream &is, vector<T> &vec){for(auto &v: vec)is >> v; return is;}
template <typename T> ostream &operator<<(ostream &os, const vector<T>& vec){for(int i = 0; i < vec.size(); i++){ os << vec[i]; if(i + 1 != vec.size())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const set<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const unordered_set<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const multiset<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &p){os << p.first << " " << p.second; return os;}
template <typename T1, typename T2> ostream &operator<<(ostream &os, const map<T1, T2> &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << itr->first << ":" << itr->second; auto titr = itr; if(++titr != mp.end())os << " "; } return os;}
template <typename T1, typename T2> ostream &operator<<(ostream &os, const unordered_map<T1, T2> &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << itr->first << ":" << itr->second; auto titr = itr; if(++titr != mp.end())os << " "; } return os;}
//  types
using ll = long long int;
using P = pair<int, int>;
// constants
const int inf = 1e9;
const ll linf = 1LL << 50;
const double EPS = 1e-10;
const int mod = 1000000007;
const int dx[4] = {-1, 0, 1, 0};
const int dy[4] = {0, -1, 0, 1};
// io
struct fast_io{
  fast_io(){ios_base::sync_with_stdio(false); cin.tie(0); cout << fixed << setprecision(20);}
} fast_io_;

template <typename T>
T power(T a, T n, T mod) {
  T res = 1;
  T tmp = n;
  T curr = a;
  while(tmp){
    if(tmp % 2 == 1){
      res = (T)(res * curr % mod);
    }
    curr = (T)(curr * curr % mod);
    tmp >>= 1;
  }

  return res;
}

struct Factorial{
  int n = 0;
  static const long long mod_default = 1e9 + 7;
  long long MOD = mod_default;
  vector<long long> fac;
  vector<long long> inv_;
  explicit Factorial(){}
  explicit Factorial(int n, long long mod_=mod_default): n(n), MOD(mod_){
    assert(MOD > 0 && n < MOD);
    fac.resize(n + 1);
    inv_.resize(n + 1);
    calc_factorial();
    calc_inv();
  }
  void calc_factorial(){
    fac[0] = 1;
    for(int i = 1; i <= n; i++){
      fac[i] = i * fac[i-1] % MOD;
    }
  }
  void calc_inv(){
    inv_[n] = power<long long>(fac[n], MOD - 2, MOD);
    for(int i = n - 1; i >= 0; i--){
      inv_[i] = (i + 1) * inv_[i+1] % MOD;
    }
  }
  long long& operator[](size_t i){
    if((int)i > n){
      cerr << "list index out of range" << endl;
      abort();
    }
    return fac[i];
  }
  long long inv(size_t i){
    if((int)i > n){
      cerr << "list index out of range" << endl;
      abort();
    }
    return inv_[i];
  }
  long long comb(int n, int k){
    if(n < 0 || k < 0 || n < k)return 0;
    long long res = fac[n];
    res = res * inv_[n-k] % MOD;
    res = res * inv_[k] % MOD;
    return res;
  }
  long long perm(int n, int k){
    if(n < 0 || k < 0 || n < k)return 0;
    long long res = fac[n];
    res = res * inv_[n-k] % MOD;
    return res;
  }
  long long h(int n, int k){
    if(n == 0 && k == 0)return 1;
    return comb(n + k - 1, k);
  }
};

template<typename T>
T gcd(T a, T b) {
  if(a > b)return gcd(b, a);
  if(a == 0)return b;
  return gcd(b % a, a);
}

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

template <typename T>
T modinv(T a, T m){
  long long x = 0, y = 0;
  extgcd<long long>(a, m, x, y);
  x %= m;
  if(x < 0)x += m;
  return x;
}

template <typename T>
map<T, int> factorize(T n){
  map<T, int> res;
  T tmp = n;
  for(T i = 2; i * i <= n; i++){
    while(tmp % i == 0){
      ++res[i];
      tmp /= i;
    }
  }
  if(tmp != 1)res[tmp] = 1;
  return res;
}


int main(int argc, char const* argv[])
{
  int k;
  cin >> k;
  vector<int> c(k);
  cin >> c;
  int csum = 0;
  rep(i, k)csum += c[i];
  Factorial fac(1000010);
  ll res = 0;
  res = fac[csum];
  rep(i, k){
    res = res * fac.inv(c[i]) % mod;
  }

  int cgcd = 0;
  rep(i, k)cgcd = gcd(cgcd, c[i]);
  auto mp = factorize(cgcd);
  irep(itr, mp){
    int sum = 0;
    ll tmp = 1;
    int i = itr->first;
    rep(j, k){
      sum += c[j] / i;
      tmp = tmp * fac.inv(c[j] / i) % mod;
    }
    tmp = tmp * fac[sum] % mod;
    if(i * 2 != csum)tmp = tmp * 2 % mod;
    res = (res + tmp) % mod;
  }

  cout << res * modinv<ll>((ll)csum, mod) % mod << endl;
  return 0;
}
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