結果

問題 No.125 悪の花弁
ユーザー keijak
提出日時 2022-03-13 19:37:13
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 124 ms / 5,000 ms
コード長 3,902 bytes
コンパイル時間 2,499 ms
コンパイル使用メモリ 212,072 KB
最終ジャッジ日時 2025-01-28 09:23:43
ジャッジサーバーID
（参考情報） 		judge4 / 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 <bits/stdc++.h>
#define REP_(i, a_, b_, a, b, ...) for (int i = (a), END_##i = (b); i < END_##i; ++i)
#define REP(i, ...) REP_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define ALL(x) std::begin(x), std::end(x)
using Int = long long;
using Uint = unsigned long long;
using Real = long double;
#include <atcoder/modint>
using Mint = atcoder::modint1000000007;
std::ostream &operator<<(std::ostream &os, const Mint &m) {
  return os << m.val();
}
template<typename T, typename U>
inline bool chmax(T &a, U b) { return a < b and ((a = b), true); }
template<typename T, typename U>
inline bool chmin(T &a, U b) { return a > b and ((a = b), true); }
template<typename T>
inline int ssize(const T &a) { return (int) a.size(); }
template<typename T>
constexpr T kBigVal = std::numeric_limits<T>::max() / 2;
template<typename T>
inline std::ostream &print_one(const T &x, char endc) {
  if constexpr (std::is_same<T, bool>::value) {
    return std::cout << (x ? "Yes" : "No") << endc;
  } else {
    return std::cout << x << endc;
  }
}
template<typename T>
inline std::ostream &print(const T &x) { return print_one(x, '\n'); }
template<typename T, typename... Ts>
std::ostream &print(const T &head, Ts... tail) {
  return print_one(head, ' '), print(tail...);
}
inline std::ostream &print() { return std::cout << '\n'; }
template<typename Container>
std::ostream &print_seq(const Container &seq,
                        const char *sep = " ",
                        const char *ends = "\n",
                        std::ostream &os = std::cout) {
  const auto itl = std::begin(seq), itr = std::end(seq);
  for (auto it = itl; it != itr; ++it) {
    if (it != itl) os << sep;
    os << *it;
  }
  return os << ends;
}
struct CastInput {
  template<typename T>
  operator T() const {
    T x;
    std::cin >> x;
    return x;
  }
  struct Sized {
    int n;
    template<typename T>
    operator T() const {
      T xs(n);
      for (auto &x: xs) std::cin >> x;
      return xs;
    }
  };
  Sized operator()(int n) const { return {n}; }
} in;
#ifdef MY_DEBUG
#include "debug_dump.hpp"
#include "backward.hpp"
backward::SignalHandling kSignalHandling;
#else
#define DUMP(...)
#define cerr if(false)cerr
#endif
// mod: prime
template<class T = Mint>
struct Factorials {
  // factorials and inverse factorials.
  std::vector<T> fact, ifact;
  // n: max cached value.
  explicit Factorials(int n) : fact(n + 1), ifact(n + 1) {
    assert(n >= 0);
    assert(n < T::mod());
    fact[0] = 1;
    for (int i = 1; i <= n; ++i) {
      fact[i] = fact[i - 1] * i;
    }
    ifact[n] = fact[n].inv();
    for (int i = n; i >= 1; --i) {
      ifact[i - 1] = ifact[i] * i;
    }
  }
  // Combination (binomial coefficients)
  T C(Int n, Int k) const {
    if (k < 0 || k > n) return 0;
    return fact[n] * ifact[k] * ifact[n - k];
  }
};
using namespace std;
std::vector<Int> divisors(Int n) {
  std::vector<Int> res;
  for (Int k = 1; k * k <= n; ++k) {
    if (n % k != 0) continue;
    res.push_back(k);
    Int q = n / k;
    if (q != k) res.push_back(q);
  }
  std::sort(res.begin(), res.end());
  return res;
}
auto solve() {
  int n = in;
  vector<int> C = in(n);
  int N = accumulate(ALL(C), 0);
  auto divs = divisors(N);
  Factorials<Mint> fs(N);
  map<Int, Mint> memo;
  auto f = [&](Int d) -> Mint {
    if (n > N / d) return 0;
    if (auto it = memo.find(d); it != memo.end()) {
      return it->second;
    }
    Mint ret = 1;
    int r = 0;
    for (Int c: C) {
      if (c % d != 0) return 0;
      ret *= fs.C(N / d - r, c / d);
      r += c / d;
    }
    memo[d] = ret;
    return ret;
  };
  Mint ans = 0;
  for (int d = 1; d <= N; ++d) {
    ans += f(N / gcd(d, N));
  }
  ans /= N;
  print(ans);
}
int main() {
  std::ios::sync_with_stdio(false), cin.tie(nullptr);
  cout << std::fixed << std::setprecision(18);
  const int T = 1;//in;
  REP(t, T) {
    (solve());
  }
}
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