#1088320 (C++23) No.1611 Minimum Multiple with Double Divisors

• 問題: No.1611 Minimum Multiple with Double Divisors
• ユーザー: kuhaku
• 提出日時: 2025-05-24 20:02:20
• 言語: C++23 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 1,286 ms / 2,000 ms
• コード長: 18,191 bytes
• コンパイル時間: 3,896 ms
• コンパイル使用メモリ: 313,480 KB
• 実行使用メモリ: 7,844 KB
• 最終ジャッジ日時: 2025-05-24 20:02:42
• 合計ジャッジ時間: 20,484 ms
• ジャッジサーバーID （参考情報）: judge5 / judge1

ファイルパターン	結果
sample	AC * 2
other	AC * 37

ソースコード

// competitive-verifier: PROBLEM
#include <algorithm>
#include <cstdint>
#include <iterator>
#include <numeric>
#include <vector>
#include <limits>
#include <utility>
namespace internal {
/// @param m `1 <= m`
/// @return x mod m
constexpr std::int64_t safe_mod(std::int64_t x, std::int64_t m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}
/// Fast modular multiplication by barrett reduction
/// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
/// NOTE: reconsider after Ice Lake
struct barrett {
    unsigned int _m;
    std::uint64_t im;
    // @param m `1 <= m`
    explicit barrett(unsigned int m) : _m(m), im((std::uint64_t)(-1) / m + 1) {}
    // @return m
    unsigned int umod() const { return _m; }
    // @param a `0 <= a < m`
    // @param b `0 <= b < m`
    // @return `a * b % m`
    unsigned int mul(unsigned int a, unsigned int b) const {
        std::uint64_t z = a;
        z *= b;
        std::uint64_t x = (std::uint64_t)(((__uint128_t)(z)*im) >> 64);
        std::uint64_t y = x * _m;
        return (unsigned int)(z - y + (z < y ? _m : 0));
    }
};
/// @brief Montgomery modular multiplication
/// @see https://rsk0315.hatenablog.com/entry/2022/11/27/060616
struct montgomery {
    /// @param m `1 <= m`
    explicit constexpr montgomery(std::uint64_t m)
        : _m(m), im(m), r((__uint128_t(1) << 64) % m), r2(-__uint128_t(m) % m) {
        for (int i = 0; i < 5; ++i) im = im * (2 - _m * im);
        im = -im;
    }
    /// @return m
    constexpr std::uint64_t umod() const { return _m; }
    /// @param a `0 <= a < m`
    /// @param b `0 <= b < m`
    /// @return `a * b % m`
    constexpr std::uint64_t mul(std::uint64_t a, std::uint64_t b) const {
        return mr((__uint128_t)a * mr((__uint128_t)b * r2));
    }
    constexpr std::uint64_t exp(std::uint64_t a, std::uint64_t b) const {
        std::uint64_t res = 1, p = mr((__uint128_t)a * r2);
        while (b) {
            if (b & 1) res = mr((__uint128_t)res * p);
            p = mr((__uint128_t)p * p);
            b >>= 1;
        }
        return res;
    }
    constexpr bool same_pow(std::uint64_t x, int s, std::uint64_t n) const {
        x = mr((__uint128_t)x * r2), n = mr((__uint128_t)n * r2);
        for (int r = 0; r < s; r++) {
            if (x == n) return true;
            x = mr((__uint128_t)x * x);
        }
        return false;
    }
  private:
    std::uint64_t _m, im, r, r2;
    constexpr std::uint64_t mr(std::uint64_t x) const {
        std::uint64_t res = (__uint128_t(x * im) * _m + x) >> 64;
        return res >= _m ? res - _m : res;
    }
    constexpr std::uint64_t mr(__uint128_t x) const {
        std::uint64_t res = (__uint128_t(std::uint64_t(x) * im) * _m + x) >> 64;
        return res >= _m ? res - _m : res;
    }
    constexpr std::uint64_t mr(std::uint64_t a, std::uint64_t b) const {
        __uint128_t t = (__uint128_t)a * b;
        std::uint64_t x = t >> 64, y = t;
        x = mr((__uint128_t)x * r), y = mr(y);
        return x + y >= _m ? x + y - _m : x + y;
    }
};
constexpr bool is_SPRP32(std::uint32_t n, std::uint32_t a) {
    std::uint32_t d = n - 1, s = 0;
    while ((d & 1) == 0) ++s, d >>= 1;
    std::uint64_t cur = 1, pw = d;
    while (pw) {
        if (pw & 1) cur = (cur * a) % n;
        a = (std::uint64_t)a * a % n;
        pw >>= 1;
    }
    if (cur == 1) return true;
    for (std::uint32_t r = 0; r < s; r++) {
        if (cur == n - 1) return true;
        cur = cur * cur % n;
    }
    return false;
}
/// given 2 <= n,a < 2^64, a prime, check whether n is a-SPRP
/// without 2,3,5,13,19,73,193,407521,299210837
constexpr bool is_SPRP64(const montgomery &m, std::uint64_t a) {
    auto n = m.umod();
    std::uint64_t d = n - 1;
    int s = 0;
    while ((d & 1) == 0) ++s, d >>= 1;
    std::uint64_t cur = m.exp(a, d);
    if (cur == 1) return true;
    return m.same_pow(cur, s, n - 1);
}
constexpr bool is_prime_constexpr(std::uint32_t x) {
    if (x == 2 || x == 3 || x == 5 || x == 7) return true;
    if (x % 2 == 0 || x % 3 == 0 || x % 5 == 0 || x % 7 == 0) return false;
    if (x < 121) return (x > 1);
    std::uint64_t h = x;
    h = ((h >> 16) ^ h) * 0x45d9f3b;
    h = ((h >> 16) ^ h) * 0x45d9f3b;
    h = ((h >> 16) ^ h) & 255;
    constexpr uint16_t bases[] = {
        15591, 2018,  166,  7429, 8064,  16045, 10503, 4399,  1949,  1295,  2776, 3620,  560,   3128,  5212,  2657,
        2300,  2021,  4652, 1471, 9336,  4018,  2398,  20462, 10277, 8028,  2213, 6219,  620,   3763,  4852,  5012,
        3185,  1333,  6227, 5298, 1074,  2391,  5113,  7061,  803,   1269,  3875, 422,   751,   580,   4729,  10239,
        746,   2951,  556,  2206, 3778,  481,   1522,  3476,  481,   2487,  3266, 5633,  488,   3373,  6441,  3344,
        17,    15105, 1490, 4154, 2036,  1882,  1813,  467,   3307,  14042, 6371, 658,   1005,  903,   737,   1887,
        7447,  1888,  2848, 1784, 7559,  3400,  951,   13969, 4304,  177,   41,   19875, 3110,  13221, 8726,  571,
        7043,  6943,  1199, 352,  6435,  165,   1169,  3315,  978,   233,   3003, 2562,  2994,  10587, 10030, 2377,
        1902,  5354,  4447, 1555, 263,   27027, 2283,  305,   669,   1912,  601,  6186,  429,   1930,  14873, 1784,
        1661,  524,   3577, 236,  2360,  6146,  2850,  55637, 1753,  4178,  8466, 222,   2579,  2743,  2031,  2226,
        2276,  374,   2132, 813,  23788, 1610,  4422,  5159,  1725,  3597,  3366, 14336, 579,   165,   1375,  10018,
        12616, 9816,  1371, 536,  1867,  10864, 857,   2206,  5788,  434,   8085, 17618, 727,   3639,  1595,  4944,
        2129,  2029,  8195, 8344, 6232,  9183,  8126,  1870,  3296,  7455,  8947, 25017, 541,   19115, 368,   566,
        5674,  411,   522,  1027, 8215,  2050,  6544,  10049, 614,   774,   2333, 3007,  35201, 4706,  1152,  1785,
        1028,  1540,  3743, 493,  4474,  2521,  26845, 8354,  864,   18915, 5465, 2447,  42,    4511,  1660,  166,
        1249,  6259,  2553, 304,  272,   7286,  73,    6554,  899,   2816,  5197, 13330, 7054,  2818,  3199,  811,
        922,   350,   7514, 4452, 3449,  2663,  4708,  418,   1621,  1171,  3471, 88,    11345, 412,   1559,  194};
    return is_SPRP32(x, bases[h]);
}
constexpr bool is_prime_constexpr(std::uint64_t x) {
    if (x <= std::numeric_limits<std::uint32_t>::max()) return is_prime_constexpr((std::uint32_t)x);
    if (x % 2 == 0 || x % 3 == 0 || x % 5 == 0 || x % 7 == 0) return false;
    montgomery m(x);
    constexpr std::uint64_t bases[] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};
    for (auto a : bases) {
        if (!is_SPRP64(m, a)) return false;
    }
    return true;
}
constexpr bool is_prime_constexpr(std::int64_t x) {
    if (x < 0) return false;
    return is_prime_constexpr(std::uint64_t(x));
}
/// @param n `0 <= n`
/// @param m `1 <= m`
/// @return `(x ** n) % m`
constexpr std::int64_t pow_mod_constexpr(std::int64_t x, std::int64_t n, int m) {
    if (m == 1) return 0;
    unsigned int _m = (unsigned int)(m);
    std::uint64_t r = 1;
    std::uint64_t y = safe_mod(x, m);
    while (n) {
        if (n & 1) r = (r * y) % _m;
        y = (y * y) % _m;
        n >>= 1;
    }
    return r;
}
/// Reference:
/// M. Forisek and J. Jancina,
/// Fast Primality Testing for Integers That Fit into a Machine Word
/// @param n `0 <= n`
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;
    std::int64_t d = n - 1;
    while (d % 2 == 0) d /= 2;
    constexpr std::int64_t bases[3] = {2, 7, 61};
    for (std::int64_t a : bases) {
        std::int64_t t = d;
        std::int64_t y = pow_mod_constexpr(a, t, n);
        while (t != n - 1 && y != 1 && y != n - 1) {
            y = y * y % n;
            t <<= 1;
        }
        if (y != n - 1 && t % 2 == 0) { return false; }
    }
    return true;
}
template <int n>
constexpr bool is_prime = is_prime_constexpr(n);
/// @param b `1 <= b`
/// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<std::int64_t, std::int64_t> inv_gcd(std::int64_t a, std::int64_t b) {
    a = safe_mod(a, b);
    if (a == 0) return {b, 0};
    std::int64_t s = b, t = a;
    std::int64_t m0 = 0, m1 = 1;
    while (t) {
        std::int64_t 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};
}
/// Compile time primitive root
/// @param m must be prime
/// @return primitive root (and minimum in now)
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; (std::int64_t)(i)*i <= x; 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);
}  // namespace internal
#include <array>
#include <bit>
/**
 * @brief 疑似乱数生成器 SplitMix64
 * @details 周期：$2^64-1$
 */
struct split_mix_64 {
    using state_type = std::uint64_t;
    using result_type = std::uint64_t;
    constexpr split_mix_64() noexcept : state(1234567890) {}
    constexpr split_mix_64(std::uint64_t seed) noexcept : state(seed) {}
    static constexpr result_type min() noexcept { return std::numeric_limits<result_type>::min(); }
    static constexpr result_type max() noexcept { return std::numeric_limits<result_type>::max(); }
    constexpr result_type operator()() {
        std::uint64_t z = (state += 0x9e3779b97f4a7c15);
        z = (z ^ (z >> 30)) * 0xbf58476d1ce4e5b9;
        z = (z ^ (z >> 27)) * 0x94d049bb133111eb;
        return z ^ (z >> 31);
    }
    constexpr state_type serialize() const noexcept { return state; }
    constexpr void deserialize(const state_type &data) noexcept { state = data; }
    constexpr void deserialize(state_type &&data) noexcept { state = std::move(data); }
    template <std::size_t N>
    constexpr std::array<std::uint64_t, N> generate_seed_sequence() noexcept {
        std::array<std::uint64_t, N> seeds = {};
        for (auto &seed : seeds) seed = operator()();
        return seeds;
    }
    /// @brief a以上b以下の整数を生成
    /// @return uint64_t [a, b]
    std::uint64_t rand_range(std::uint64_t a, std::uint64_t b) {
        if (a == split_mix_64::min() && b == split_mix_64::max()) return operator()();
        return a + operator()() % (b - a + 1);
    }
    /// @brief 0.0以上1.0未満の浮動小数点数を生成
    /// @return double [0, 1)
    double random() { return (double)operator()() / max(); }
  private:
    state_type state;
};
/// @brief 疑似乱数生成器 xoroshiro128++
struct xoroshiro128 {
    using state_type = std::array<std::uint64_t, 2>;
    using result_type = std::uint64_t;
    constexpr xoroshiro128() noexcept : state(split_mix_64{}.generate_seed_sequence<2>()) {}
    constexpr xoroshiro128(std::uint64_t seed) noexcept : state(split_mix_64{seed}.generate_seed_sequence<2>()) {}
    static constexpr result_type min() noexcept { return std::numeric_limits<result_type>::min(); }
    static constexpr result_type max() noexcept { return std::numeric_limits<result_type>::max(); }
    constexpr result_type operator()() {
        const std::uint64_t s0 = state[0];
        std::uint64_t s1 = state[1];
        const std::uint64_t result = std::rotl(s0 + s1, 17) + s0;
        s1 ^= s0;
        state[0] = std::rotl(s0, 49) ^ s1 ^ (s1 << 21), state[1] = std::rotl(s1, 28);
        return result;
    }
    bool operator==(const xoroshiro128 &rhs) noexcept { return (state == rhs.state); }
    bool operator!=(const xoroshiro128 &rhs) noexcept { return (state != rhs.state); }
    constexpr state_type serialize() const noexcept { return state; }
    constexpr void deserialize(const state_type &data) noexcept { state = data; }
    constexpr void deserialize(state_type &&data) noexcept { state = std::move(data); }
    /// @brief a以上b以下の整数を生成
    /// @return uint64_t [a, b]
    std::uint64_t rand_range(std::uint64_t a, std::uint64_t b) {
        if (a == xoroshiro128::min() && b == xoroshiro128::max()) return operator()();
        return a + operator()() % (b - a + 1);
    }
    /// @brief 0.0以上1.0未満の浮動小数点数を生成
    /// @return double [0, 1)
    double random() noexcept { return (double)operator()() / max(); }
  private:
    state_type state;
};
namespace internal {
std::uint64_t pollard_rho(std::uint64_t n) {
    static xoroshiro128 rnd;
    if (~n & 1) return 2;
    if (internal::is_prime_constexpr(n)) return n;
    std::uint64_t r = 0, g = 1;
    auto f = [&](std::uint64_t x) -> std::uint64_t { return ((__uint128_t)x * x + r) % n; };
    std::uniform_int_distribution<std::uint64_t> gen(2, n - 1);
    while (true) {
        std::uint64_t x, y, z, ys, q = 1;
        r = gen(rnd), y = gen(rnd);
        g = 1;
        constexpr int m = 128;
        for (int r = 1; g == 1; r <<= 1) {
            x = y;
            for (int i = 0; i < r; ++i) y = f(y);
            for (int k = 0; g == 1 && k < r; k += m) {
                ys = y;
                for (int i = 0; i < m && i < r - k; ++i) q = (__uint128_t)q * (x + n - (y = f(y))) % n;
                g = std::gcd(q, n);
            }
        }
        if (g == n) {
            do {
                z = x + n - (ys = f(ys));
                if (z >= n) z -= n;
                g = std::gcd(z, n);
            } while (g == 1);
        }
        if (g != n) break;
    }
    return g;
}
std::vector<std::uint64_t> inner_factorize(std::uint64_t n) {
    if (n <= 1) return {};
    std::uint64_t p = pollard_rho(n);
    if (p == n) return {p};
    auto l = inner_factorize(p);
    auto r = inner_factorize(n / p);
    std::copy(r.begin(), r.end(), std::back_inserter(l));
    return l;
}
}  // namespace internal
/// @brief 素因数分解
std::vector<std::uint64_t> factorize(std::uint64_t n) {
    auto res = internal::inner_factorize(n);
    std::sort(res.begin(), res.end());
    return res;
}
std::uint64_t number_of_divisors(std::vector<std::uint64_t> v) {
    std::sort(v.begin(), v.end());
    int n = v.size();
    int c = 0;
    std::uint64_t res = 1;
    for (int i = 0; i < n; ++i) {
        if (i == 0 || v[i] == v[i - 1]) {
            ++c;
        } else {
            res *= c + 1;
            c = 1;
        }
    }
    return res * (c + 1);
}
#ifdef ATCODER
#pragma GCC target("sse4.2,avx512f,avx512dq,avx512ifma,avx512cd,avx512bw,avx512vl,bmi2")
#endif
#pragma GCC optimize("Ofast,fast-math,unroll-all-loops")
#include <bits/stdc++.h>
#ifndef ATCODER
#pragma GCC target("sse4.2,avx2,bmi2")
#endif
template <class T, class U>
constexpr bool chmax(T &a, const U &b) {
    return a < (T)b ? a = (T)b, true : false;
}
template <class T, class U>
constexpr bool chmin(T &a, const U &b) {
    return (T)b < a ? a = (T)b, true : false;
}
constexpr std::int64_t INF = 1000000000000000003;
constexpr int Inf = 1000000003;
constexpr double EPS = 1e-7;
constexpr double PI = 3.14159265358979323846;
#define FOR(i, m, n) for (int i = (m); i < int(n); ++i)
#define FORR(i, m, n) for (int i = (m)-1; i >= int(n); --i)
#define FORL(i, m, n) for (int64_t i = (m); i < int64_t(n); ++i)
#define rep(i, n) FOR (i, 0, n)
#define repn(i, n) FOR (i, 1, n + 1)
#define repr(i, n) FORR (i, n, 0)
#define repnr(i, n) FORR (i, n + 1, 1)
#define all(s) (s).begin(), (s).end()
struct Sonic {
    Sonic() {
        std::ios::sync_with_stdio(false);
        std::cin.tie(nullptr);
        std::cout << std::fixed << std::setprecision(20);
    }
    constexpr void operator()() const {}
} sonic;
using namespace std;
using ll = std::int64_t;
using ld = long double;
template <class T, class U>
std::istream &operator>>(std::istream &is, std::pair<T, U> &p) {
    return is >> p.first >> p.second;
}
template <class T>
std::istream &operator>>(std::istream &is, std::vector<T> &v) {
    for (T &i : v) is >> i;
    return is;
}
template <class T, class U>
std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &p) {
    return os << '(' << p.first << ',' << p.second << ')';
}
template <class T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &v) {
    for (auto it = v.begin(); it != v.end(); ++it) os << (it == v.begin() ? "" : " ") << *it;
    return os;
}
template <class Head, class... Tail>
void co(Head &&head, Tail &&...tail) {
    if constexpr (sizeof...(tail) == 0) std::cout << head << '\n';
    else std::cout << head << ' ', co(std::forward<Tail>(tail)...);
}
template <class Head, class... Tail>
void ce(Head &&head, Tail &&...tail) {
    if constexpr (sizeof...(tail) == 0) std::cerr << head << '\n';
    else std::cerr << head << ' ', ce(std::forward<Tail>(tail)...);
}
void Yes(bool is_correct = true) { std::cout << (is_correct ? "Yes\n" : "No\n"); }
void No(bool is_not_correct = true) { Yes(!is_not_correct); }
void YES(bool is_correct = true) { std::cout << (is_correct ? "YES\n" : "NO\n"); }
void NO(bool is_not_correct = true) { YES(!is_not_correct); }
void Takahashi(bool is_correct = true) { std::cout << (is_correct ? "Takahashi" : "Aoki") << '\n'; }
void Aoki(bool is_not_correct = true) { Takahashi(!is_not_correct); }
int main(void) {
    int t;
    cin >> t;
    while (t--) {
        uint64_t x;
        cin >> x;
        auto v = factorize(x);
        auto c = number_of_divisors(v);
        FOR (i, 2, 32) {
            auto u = factorize(i);
            u.insert(u.end(), v.begin(), v.end());
            if (number_of_divisors(u) == c * 2) {
                co(x * i);
                break;
            }
        }
    }
    return 0;
}