#483207 (C++14) No.125 悪の花弁

• 問題: No.125 悪の花弁
• ユーザー: maine_honzuki
• 提出日時: 2020-05-17 20:55:34
• 言語: C++14 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 152 ms / 5,000 ms
• コード長: 2,926 bytes
• コンパイル時間: 1,723 ms
• コンパイル使用メモリ: 177,544 KB
• 実行使用メモリ: 15,896 KB
• 最終ジャッジ日時: 2024-10-01 07:03:55
• 合計ジャッジ時間: 3,017 ms
• ジャッジサーバーID （参考情報）: judge1 / judge2

ファイルパターン	結果
other	AC * 6

ソースコード

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#include <bits/stdc++.h>
using namespace std;
const int MOD = 1e9 + 7;
using ll = long long;
using ull = unsigned long long;
template <uint MD>
struct ModInt {
    using M = ModInt;
    const static M G;
    uint v;
    ModInt(ll _v = 0) { set_v(_v % MD + MD); }
    M& set_v(uint _v) {
        v = (_v < MD) ? _v : _v - MD;
        return *this;
    }
    explicit operator bool() const { return v != 0; }
    M operator-() const { return M() - *this; }
    M operator+(const M& r) const { return M().set_v(v + r.v); }
    M operator-(const M& r) const { return M().set_v(v + MD - r.v); }
    M operator*(const M& r) const { return M().set_v(ull(v) * r.v % MD); }
    M operator/(const M& r) const { return *this * r.inv(); }
    M& operator+=(const M& r) { return *this = *this + r; }
    M& operator-=(const M& r) { return *this = *this - r; }
    M& operator*=(const M& r) { return *this = *this * r; }
    M& operator/=(const M& r) { return *this = *this / r; }
    bool operator==(const M& r) const { return v == r.v; }
    M pow(ll n) const {
        M x = *this, r = 1;
        while (n) {
            if (n & 1)
                r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    M inv() const { return pow(MD - 2); }
    friend ostream& operator<<(ostream& os, const M& r) { return os << r.v; }
    friend istream& operator>>(istream& is, M& r) { return is >> r.v; }
};
using Mint = ModInt<MOD>;
vector<int> divisor(int n) {
    vector<int> ret;
    for (int i = 1; i * i <= n; i++) {
        if (n % i == 0) {
            ret.push_back(i);
            if (i * i != n)
                ret.push_back(n / i);
        }
    }
    sort(begin(ret), end(ret));
    return (ret);
}
int gcd(int a, int b) {
    while (b) {
        int c = b;
        b = a % b;
        a = c;
    }
    return a;
}
const int MN = 1'000'010;
Mint fact[MN], iFac[MN];
void first() {
    fact[0] = Mint(1);
    for (int i = 1; i < MN; i++)
        fact[i] = fact[i - 1] * Mint(i);
    iFac[MN - 1] = fact[MN - 1].inv();
    for (int i = MN - 1; i >= 1; i--) {
        iFac[i - 1] = iFac[i] * Mint(i);
    }
    assert(fact[2345] * iFac[2345] == Mint(1));
}
int main() {
    first();
    int K, total = 0;
    cin >> K;
    vector<int> C(K);
    for (int i = 0; i < K; i++) {
        cin >> C[i];
        total += C[i];
    }
    int GCD = C[0];
    for (int i = 1; i < K; i++) {
        GCD = gcd(GCD, C[i]);
    }
    auto V = divisor(GCD);
    vector<Mint> memo(total + 1);
    for (auto& x : V) {
        auto c = C;
        int SUM = 0;
        for (auto& a : c) {
            a /= x;
            SUM += a;
        }
        Mint tmp = fact[SUM];
        for (auto& a : c) {
            tmp *= iFac[a];
        }
        memo[total / x] = tmp;
    }
    Mint ans = 0;
    for (int i = 1; i <= total; i++) {
        ans += memo[gcd(i, total)];
    }
    ans /= total;
    cout << ans << endl;
}
 
 
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