結果

問題 No.181 A↑↑N mod M
コンテスト
ユーザー leeh18
提出日時 2022-12-02 16:50:56
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 2 ms / 5,000 ms
コード長 3,468 bytes
コンパイル時間 2,418 ms
コンパイル使用メモリ 206,920 KB
最終ジャッジ日時 2025-02-09 03:13:09
ジャッジサーバーID
（参考情報） 		judge1 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 6
other AC * 37
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 #
raw source code 

#include <bits/stdc++.h>

unsigned long long modmul(unsigned long long a, unsigned long long b,
                          unsigned long long M) {
    long long ret =
        a * b - M * static_cast<unsigned long long>(1.L / M * a * b);
    return ret + M * (ret < 0) - M * (ret >= static_cast<long long>(M));
}

unsigned long long modpow(unsigned long long b, unsigned long long e,
                          unsigned long long mod) {
    unsigned long long ans = 1;
    for (; e; b = modmul(b, b, mod), e /= 2) {
        if (e & 1) {
            ans = modmul(ans, b, mod);
        }
    }
    return ans;
}

bool is_prime(unsigned long long n) {
    if (n < 2 || n % 6 % 4 != 1) {
        return (n | 1) == 3;
    }
    unsigned long long A[] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022},
                       s = __builtin_ctzll(n - 1), d = n >> s;
    for (unsigned long long a : A) {
        unsigned long long p = modpow(a % n, d, n), i = s;
        while (p != 1 && p != n - 1 && a % n && i--) {
            p = modmul(p, p, n);
        }
        if (p != n - 1 && i != s) {
            return 0;
        }
    }
    return 1;
}

unsigned long long pollard(unsigned long long n) {
    auto f = [n](unsigned long long x) { return modmul(x, x, n) + 1; };
    unsigned long long x = 0, y = 0, t = 30, prd = 2, i = 1, q;
    while (t++ % 40 || std::gcd(prd, n) == 1) {
        if (x == y) {
            x = ++i, y = f(x);
        }
        if ((q = modmul(prd, std::max(x, y) - std::min(x, y), n))) {
            prd = q;
        }
        x = f(x), y = f(f(y));
    }
    return std::gcd(prd, n);
}

std::vector<unsigned long long> factor(unsigned long long n) {
    if (n == 1) {
        return {};
    }
    if (is_prime(n)) {
        return {n};
    }
    unsigned long long x = pollard(n);
    auto l = factor(x), r = factor(n / x);
    l.insert(l.end(), r.begin(), r.end());
    return l;
}

unsigned long long euler_phi(unsigned long long n) {
    auto f = factor(n);
    std::sort(f.begin(), f.end());
    f.erase(std::unique(f.begin(), f.end()), f.end());
    for (auto p : f) {
        n -= n / p;
    }
    return n;
}


template <typename T, typename Promote = unsigned long long>
T power_tower(const std::vector<T> &a, T m) {
    static_assert(std::is_integral_v<T>);
    assert(m > 0);
    std::vector<unsigned long long> mod_chain{
        static_cast<unsigned long long>(m)};
    while (mod_chain.back() > 1) {
        const auto phi = euler_phi(mod_chain.back());
        mod_chain.push_back(phi);
    }
    const auto f = [](Promote x, Promote n, Promote mod) {
        Promote r = 1;
        if (x > mod) {
            x = x % mod + mod;
        }
        while (n) {
            if (n & 1) {
                r *= x;
                if (r > mod) {
                    r = r % mod + mod;
                }
            }
            x *= x;
            if (x > mod) {
                x = x % mod + mod;
            }
            n >>= 1;
        }
        return r;
    };
    Promote r = 1;
    const auto k = static_cast<int>(std::min(a.size(), mod_chain.size()));
    for (auto i = k - 1; i >= 0; --i) {
        assert(a[i] > 0);
        r = f(static_cast<Promote>(a[i]), r, mod_chain[i]);
    }
    return static_cast<T>(r % static_cast<Promote>(m));
}

int main() {
    std::cin.tie(0)->sync_with_stdio(0);
    int A, N, M;
    std::cin >> A >> N >> M;
    std::vector<int> a(std::min(N, 24), A);
    std::cout << power_tower(a, M);
}
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