結果

問題 No.1844 Divisors Sum Sum
コンテスト
ユーザー ooaiu
提出日時 2025-07-24 22:55:06
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 107 ms / 3,000 ms
コード長 7,881 bytes
コンパイル時間 3,222 ms
コンパイル使用メモリ 279,260 KB
実行使用メモリ 7,716 KB
最終ジャッジ日時 2025-07-24 22:55:14
合計ジャッジ時間 8,004 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge2
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
other AC * 38
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 # 

#include <bits/stdc++.h>
using namespace std;
template <class F> class y_combinator {
    F f;

   public:
    y_combinator(F&& f) : f(std::forward<F>(f)) {}
    template <class... Args> auto operator()(Args&&... args) const { return f(*this, std::forward<Args>(args)...); }
};
using ll = long long;
using ld = long double;
template <class T, class U = std::less<T>> using prique = std::priority_queue<T, std::vector<T>, U>;
template <class T> T floor(T a, T b) noexcept { return a / b - (a % b && (a ^ b) < 0); }
template <class T> T ceil(T a, T b) noexcept { return floor(a + b - 1, b); }
template <class T> bool chmin(T& x, const T& y) noexcept { return (x > y ? x = y, true : false); }
template <class T> bool chmax(T& x, const T& y) noexcept { return (x < y ? x = y, true : false); }
#define overload4(a, b, c, d, e, ...) e
#define rep1(a) for (long long _i = 0; _i < (a); _i++)
#define rep2(i, a) for (long long i = 0; i < (a); i++)
#define rep3(i, a, b) for (long long i = (a); i < (b); i++)
#define rep4(i, a, b, c) for (long long i = (a); i < (b); i += (c))
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define rrep(i, a, b, c) for (long long i = (a); i > (b); i += (c))
#define all(x) std::begin(x), std::end(x)
#define rall(x) std::rbegin(x), std::rend(x)
#define pb push_back
#ifndef LOCAL
#define debug(...)
#endif

namespace internal {

constexpr long long safe_mod(long long x, long long m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}

constexpr long long pow_mod_constexpr(long long x, long long n, int m_) {
    if (m_ == 1) return 0;
    unsigned int m = static_cast<unsigned int>(m_);
    unsigned long long r = 1, y = safe_mod(x, m);
    while (n) {
        if (n & 1) {
            r = (r * y) % m;
        }
        y = (y * y) % m;
        n >>= 1;
    }
    return r;
}

constexpr bool is_prime_constexpr(int n) {
    if (n <= 1) return false;
    if (n == 2 || n == 7 || n == 61) return true;
    if (n % 2 == 0) return false;
    long long t = n - 1;
    while (t % 2 == 0) t /= 2;
    constexpr long long base[3] = {2, 7, 61};
    for (long long a : base) {
        long long d = t;
        long long v = pow_mod_constexpr(a, t, n);
        if (v == 1) continue;
        while (d != n - 1 && v != n - 1) {
            v = v * v % n;
            d <<= 1;
        }
        if (v != n - 1) return false;
    }
    return true;
}
template <int n>
constexpr bool is_prime = is_prime_constexpr(n);

constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
    a = safe_mod(a, b);
    if (a == 0) return {b, 0};

    long long s = b, t = a;
    long long m0 = 0, m1 = 1;

    while (t) {
        long long u = s / t;
        s -= t * u;
        m0 -= m1 * u;

        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}

constexpr long long inv_mod(long long x, long long m) {
    assert(1 <= m);
    auto z = inv_gcd(x, m);
    assert(z.first == 1);
    return z.second;
}

constexpr int primitive_root_constexpr(int m) {
    if (m == 2) return 1;
    if (m == 167772161) return 3;
    if (m == 469762049) return 3;
    if (m == 754974721) return 11;
    if (m == 998244353) return 3;
    int divs[20] = {};
    divs[0] = 2;
    int cnt = 1;
    int x = (m - 1) / 2;
    while (x % 2 == 0) x /= 2;
    for (int i = 3; i <= x / i; i += 2) {
        if (x % i == 0) {
            divs[cnt++] = i;
            while (x % i == 0) x /= i;
        }
    }
    if (x > 1) divs[cnt++] = x;
    for (int g = 2;; g++) {
        bool ok = true;
        for (int i = 0; i < cnt; i++) {
            if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return g;
    }
}
template <int m>
constexpr int primitive_root = primitive_root_constexpr(m);

unsigned long long floor_sum_unsigned(unsigned long long n,
                                      unsigned long long m,
                                      unsigned long long a,
                                      unsigned long long b) {
    unsigned long long ans = 0;
    while (true) {
        if (a >= m) {
            ans += n * (n - 1) / 2 * (a / m);
            a %= m;
        }
        if (b >= m) {
            ans += n * (b / m);
            b %= m;
        }

        unsigned long long y_max = a * n + b;
        if (y_max < m) break;
        n = (unsigned long long)(y_max / m);
        b = (unsigned long long)(y_max % m);
        std::swap(m, a);
    }
    return ans;
}

}  // namespace internal

template <unsigned m>
class StaticModint {
    unsigned value;
    using mint = StaticModint;
    static constexpr bool is_prime = internal::is_prime<m>;
    static constexpr unsigned umod() { return m; }

   public:
    static constexpr unsigned mod() { return m; }
    static mint raw(int v) {
        mint x;
        x.value = v;
        return x;
    }

    StaticModint() : value(0) {}
    template <class T, std::enable_if_t<std::is_integral_v<T>, int> = false>
    StaticModint(T v) { value = static_cast<unsigned>(internal::safe_mod(v, m)); }

    int val() const { return value; }
    mint& operator++() {
        value = (value + 1 == umod() ? 0 : value + 1);
        return *this;
    }
    mint& operator--() {
        value = (value == 0 ? umod() - 1 : value - 1);
        return *this;
    }
    mint operator++(int) {
        mint res = *this;
        ++*this;
        return res;
    }
    mint operator--(int) {
        mint res = *this;
        --*this;
        return res;
    }
    mint& operator+=(const mint& rhs) {
        value += rhs.value;
        if (value >= umod()) value -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        if (value < rhs.value) value += umod();
        value -= rhs.value;
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        unsigned long long z = value;
        z *= rhs.value;
        value = static_cast<unsigned>(z % umod());
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }
    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        for (; n; n >>= 1, x *= x)
            if (n & 1) r *= x;
        return r;
    }
    mint inv() const { return (is_prime ? pow(m - 2) : internal::inv_mod(value, m)); }
    friend mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; }
    friend mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; }
    friend mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; }
    friend mint operator/(const mint& lhs, const mint& rhs) { return mint(lhs) /= rhs; }
    friend bool operator==(const mint& lhs, const mint& rhs) { return lhs.value == rhs.value; }
    friend bool operator!=(const mint& lhs, const mint& rhs) { return lhs.value != rhs.value; }
    template <class Pr> void print(Pr& p) const { p << value; }
    template <class Sc> void scan(Sc& s) { s >> value; }
};

using modint998 = StaticModint<998244353>;
using modint107 = StaticModint<1000000007>;

using mint = modint107;
void run_case() {
    int L;
    cin >> L;
    vector<int> P(L), E(L);
    rep(i, L) cin >> P[i] >> E[i];
    mint ans = 1;
    rep(i, L) {
        mint cur = mint::raw(P[i]).pow(E[i] + 2) - P[i];
        const mint inv = mint::raw(P[i] - 1).inv();
        cur *= inv;
        cur -= E[i] + 1;
        cur *= inv;
        ans *= cur;
    }
    cout << ans.val() << "\n";
}
int main() {
    std::ios_base::sync_with_stdio(false);
    std::cin.tie(nullptr);
    std::fixed(std::cout).precision(16);
    int T = 1;
    while (T--) run_case();
    return 0;
}
0