結果

問題 No.125 悪の花弁
ユーザー fine
提出日時 2020-07-07 01:30:46
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 79 ms / 5,000 ms
コード長 5,566 bytes
コンパイル時間 1,919 ms
コンパイル使用メモリ 177,256 KB
実行使用メモリ 19,244 KB
最終ジャッジ日時 2024-09-25 02:11:57
合計ジャッジ時間 2,522 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge5
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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>
using namespace std;
using ll = long long;
constexpr char newl = '\n';
// https://noshi91.hatenablog.com/entry/2019/03/31/174006
template <std::uint_fast64_t Modulus>
struct ModInt {
    using u64 = std::uint_fast64_t;
    static constexpr u64 MOD = Modulus;
    u64 val;
    constexpr ModInt(const u64 x = 0) noexcept : val(x % MOD) {}
    constexpr ModInt operator+() const noexcept { return ModInt(*this); }
    constexpr ModInt operator-() const noexcept {
        ModInt res(*this);
        if (res.val != 0) res.val = MOD - res.val;
        return res;
    }
    constexpr bool operator==(const ModInt& rhs) const noexcept { return val == rhs.val; }
    constexpr bool operator!=(const ModInt& rhs) const noexcept { return val != rhs.val; }
    // prefix increment/decrement
    constexpr ModInt& operator++() noexcept { return *this += ModInt(1); }
    constexpr ModInt& operator--() noexcept { return *this -= ModInt(1); }
    // postfix increment/decrement
    constexpr ModInt operator++(int) noexcept {
        ModInt tmp(*this);
        ++*this;
        return tmp;
    }
    constexpr ModInt operator--(int) noexcept {
        ModInt tmp(*this);
        --*this;
        return tmp;
    }
    constexpr ModInt operator+(const ModInt& rhs) const noexcept {
        return ModInt(*this) += rhs;
    }
    constexpr ModInt operator-(const ModInt& rhs) const noexcept {
        return ModInt(*this) -= rhs;
    }
    constexpr ModInt operator*(const ModInt& rhs) const noexcept {
        return ModInt(*this) *= rhs;
    }
    constexpr ModInt operator/(const ModInt& rhs) const noexcept {
        return ModInt(*this) /= rhs;
    }
    constexpr ModInt& operator+=(const ModInt& rhs) noexcept {
        val += rhs.val;
        if (val >= MOD) val -= MOD;
        return *this;
    }
    constexpr ModInt& operator-=(const ModInt& rhs) noexcept {
        if (val < rhs.val) val += MOD;
        val -= rhs.val;
        return *this;
    }
    constexpr ModInt& operator*=(const ModInt& rhs) noexcept {
        val = val * rhs.val % MOD;
        return *this;
    }
    // prime Modulus only
    constexpr ModInt& operator/=(const ModInt& rhs) noexcept {
        return *this *= rhs.inv();
    }
    // prime Modulus only
    constexpr ModInt inv() const noexcept {
        return pow(*this, MOD - 2);
    }
};
template<std::uint_fast64_t Modulus>
constexpr ModInt<Modulus> pow(ModInt<Modulus> x, std::uint_fast64_t n) {
    ModInt<Modulus> res(1);
    while (n) {
        if (n & 1) res *= x;
        x *= x;
        n >>= 1;
    }
    return res;
}
template<std::uint_fast64_t Modulus>
istream& operator>>(istream& is, ModInt<Modulus>& x) {
    std::uint_fast64_t val;
    is >> val;
    x = ModInt<Modulus>(val);
    return is;
}
template<std::uint_fast64_t Modulus>
ostream& operator<<(ostream& os, const ModInt<Modulus>& x) {
    return os << x.val;
}
using mint = ModInt<1000000007>;
// g++ -Wl,--stack,[STACK SIZE] [file] でスタックサイズを増やすか、
// グローバル変数として宣言して使うこと！！！
template<size_t MAXV, class T = mint>
struct Comb {
    array<T, MAXV + 1> fact, fact_inv;
    constexpr Comb() noexcept {
        fact[0] = 1;
        for (size_t i = 1; i <= MAXV; i++) {
            fact[i] = fact[i - 1] * i;
        }
        fact_inv[MAXV] = fact[MAXV].inv();
        for (size_t i = MAXV; i > 0; i--) {
            fact_inv[i - 1] = fact_inv[i] * i;
        }
    }
    constexpr T operator()(int n, int k) const noexcept {
        if (n < k || n < 0 || k < 0) return 0;
        return fact[n] * fact_inv[k] * fact_inv[n - k];
    }
    constexpr T perm(int n, int k) const noexcept {
        if (n < k || n < 0 || k < 0) return 0;
        return fact[n] * fact_inv[n - k];
    }
};
const Comb<1000000> comb;
template<typename T>
vector<T> divisor(T n) {
    vector<T> res;
    for (T i = 1; i * i <= n; i++) {
        if (n % i == 0) {
            res.emplace_back(i);
            if (i != n / i) res.emplace_back(n / i);
        }
    }
    return res;
}
/*
map<int, int> moebius(int n) {
    map<int, int> res;
    vector<int> primes;
    for (int i = 2; i * i <= n; i++) {
        if (n % i == 0) {
            primes.push_back(i);
            while (n % i == 0) n /= i;
        }
    }
    if (n != 1) primes.push_back(n);
    int m = primes.size();
    for (int i = 0; i < (1 << m); i++) {
        int mu = 1, d = 1;
        for (int j = 0; j < m; j++) {
            if (i >> j & 1) {
                mu *= -1;
                d *= primes[j];
            }
        }
        res[d] = mu;
    }
    return res;
}*/
int main() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    int K;
    cin >> K;
    int sum = 0;
    vector<int> c(K);
    for (int i = 0; i < K; i++) {
        cin >> c[i];
        sum += c[i];
    }
    int g = sum;
    for (int i = 0; i < K; i++) {
        g = __gcd(g, c[i]);
    }
    vector<int> v = divisor(g);
    sort(v.begin(), v.end());
    int sz = v.size();
    // map<int, int> meb = moebius(sum);
    mint ans = 0;
    vector<mint> dp(sz, 0);
    for (int i = sz - 1; i >= 0; i--) {
        int d = v[i];
        int num = sum / d;
        dp[i] = comb.fact[num];
        for (int j = 0; j < K; j++) {
            dp[i] /= comb.fact[c[j] / d];
        }
        for (int j = i + 1; j < sz; j++) {
            int num2 = sum / v[j];
            if (num % num2 != 0) continue;
            dp[i] -= dp[j];
        }
        ans += dp[i] / num;
    }
    cout << ans << newl;
    return 0;
}
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