結果

問題 No.2682 Visible Divisible
コンテスト
ユーザー udon1206
提出日時 2024-03-20 22:21:02
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 72 ms / 2,000 ms
コード長 6,835 bytes
コンパイル時間 2,374 ms
コンパイル使用メモリ 210,596 KB
最終ジャッジ日時 2025-02-20 09:24:54
ジャッジサーバーID
（参考情報） 		judge2 / judge2
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ファイルパターン 結果
sample AC * 3
other AC * 14
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 ll = long long;
using std::cin;
using std::cout;
using std::endl;

std::mt19937 rnd(std::chrono::steady_clock::now().time_since_epoch().count());
template <class T>
inline bool chmax(T &a, T b)
{
    if (a < b)
    {
        a = b;
        return 1;
    }
    return 0;
}
template <class T>
inline bool chmin(T &a, T b)
{
    if (a > b)
    {
        a = b;
        return 1;
    }
    return 0;
}

constexpr int inf = (int)1e9 + 7;
constexpr long long INF = 1LL << 60;

namespace FastPrimeFactorization
{
    using namespace std;
    template <typename word, typename dword, typename sword>
    struct UnsafeMod
    {
        UnsafeMod() : x(0) {}

        UnsafeMod(word _x) : x(init(_x)) {}

        bool operator==(const UnsafeMod &rhs) const
        {
            return x == rhs.x;
        }

        bool operator!=(const UnsafeMod &rhs) const
        {
            return x != rhs.x;
        }

        UnsafeMod &operator+=(const UnsafeMod &rhs)
        {
            if ((x += rhs.x) >= mod)
                x -= mod;
            return *this;
        }

        UnsafeMod &operator-=(const UnsafeMod &rhs)
        {
            if (sword(x -= rhs.x) < 0)
                x += mod;
            return *this;
        }

        UnsafeMod &operator*=(const UnsafeMod &rhs)
        {
            x = reduce(dword(x) * rhs.x);
            return *this;
        }

        UnsafeMod operator+(const UnsafeMod &rhs) const
        {
            return UnsafeMod(*this) += rhs;
        }

        UnsafeMod operator-(const UnsafeMod &rhs) const
        {
            return UnsafeMod(*this) -= rhs;
        }

        UnsafeMod operator*(const UnsafeMod &rhs) const
        {
            return UnsafeMod(*this) *= rhs;
        }

        UnsafeMod pow(uint64_t e) const
        {
            UnsafeMod ret(1);
            for (UnsafeMod base = *this; e; e >>= 1, base *= base)
            {
                if (e & 1)
                    ret *= base;
            }
            return ret;
        }

        word get() const
        {
            return reduce(x);
        }

        static constexpr int word_bits = sizeof(word) * 8;

        static word modulus()
        {
            return mod;
        }

        static word init(word w)
        {
            return reduce(dword(w) * r2);
        }

        static void set_mod(word m)
        {
            mod = m;
            inv = mul_inv(mod);
            r2 = -dword(mod) % mod;
        }

        static word reduce(dword x)
        {
            word y = word(x >> word_bits) - word((dword(word(x) * inv) * mod) >> word_bits);
            return sword(y) < 0 ? y + mod : y;
        }

        static word mul_inv(word n, int e = 6, word x = 1)
        {
            return !e ? x : mul_inv(n, e - 1, x * (2 - x * n));
        }

        static word mod, inv, r2;

        word x;
    };

    using uint128_t = __uint128_t;

    using Mod64 = UnsafeMod<uint64_t, uint128_t, int64_t>;
    template <>
    uint64_t Mod64::mod = 0;
    template <>
    uint64_t Mod64::inv = 0;
    template <>
    uint64_t Mod64::r2 = 0;

    using Mod32 = UnsafeMod<uint32_t, uint64_t, int32_t>;
    template <>
    uint32_t Mod32::mod = 0;
    template <>
    uint32_t Mod32::inv = 0;
    template <>
    uint32_t Mod32::r2 = 0;

    bool miller_rabin_primality_test_uint64(uint64_t n)
    {
        Mod64::set_mod(n);
        uint64_t d = n - 1;
        while (d % 2 == 0)
            d /= 2;
        Mod64 e{1}, rev{n - 1};
        // http://miller-rabin.appspot.com/  < 2^64
        for (uint64_t a : {2, 325, 9375, 28178, 450775, 9780504, 1795265022})
        {
            if (n <= a)
                break;
            uint64_t t = d;
            Mod64 y = Mod64(a).pow(t);
            while (t != n - 1 && y != e && y != rev)
            {
                y *= y;
                t *= 2;
            }
            if (y != rev && t % 2 == 0)
                return false;
        }
        return true;
    }

    bool miller_rabin_primality_test_uint32(uint32_t n)
    {
        Mod32::set_mod(n);
        uint32_t d = n - 1;
        while (d % 2 == 0)
            d /= 2;
        Mod32 e{1}, rev{n - 1};
        for (uint32_t a : {2, 7, 61})
        {
            if (n <= a)
                break;
            uint32_t t = d;
            Mod32 y = Mod32(a).pow(t);
            while (t != n - 1 && y != e && y != rev)
            {
                y *= y;
                t *= 2;
            }
            if (y != rev && t % 2 == 0)
                return false;
        }
        return true;
    }

    bool is_prime(uint64_t n)
    {
        if (n == 2)
            return true;
        if (n == 1 || n % 2 == 0)
            return false;
        if (n < uint64_t(1) << 31)
            return miller_rabin_primality_test_uint32(n);
        return miller_rabin_primality_test_uint64(n);
    }

    uint64_t pollard_rho(uint64_t n)
    {
        if (is_prime(n))
            return n;
        if (n % 2 == 0)
            return 2;
        Mod64::set_mod(n);
        uint64_t d;
        Mod64 one{1};
        for (Mod64 c{one};; c += one)
        {
            Mod64 x{2}, y{2};
            do
            {
                x = x * x + c;
                y = y * y + c;
                y = y * y + c;
                d = __gcd((x - y).get(), n);
            } while (d == 1);
            if (d < n)
                return d;
        }
        assert(0);
    }

    vector<uint64_t> prime_factor(uint64_t n)
    {
        if (n <= 1)
            return {};
        uint64_t p = pollard_rho(n);
        if (p == n)
            return {p};
        auto l = prime_factor(p);
        auto r = prime_factor(n / p);
        copy(begin(r), end(r), back_inserter(l));
        return l;
    }
};

void solve()
{

    ll n, K;
    cin >> n >> K;
    std::vector<ll> a(n);
    for (int i = 0; i < n; i++)
    {
        cin >> a[i];
    }

    std::map<ll, ll> prime_factors;
    {
        auto prime_factors_ = FastPrimeFactorization::prime_factor(K);
        for (auto &p : prime_factors_)
        {
            prime_factors[p]++;
        }
    }
    std::map<ll, ll> cnt;
    for (const auto &e : a)
    {
        ll t = e;
        for (const auto &p : prime_factors)
        {
            int c = 0;
            while (t % p.first == 0)
            {
                t /= p.first;
                c++;
            }
            chmax(cnt[p.first], (ll)c);
        }
    }
    for (const auto &[p, c] : prime_factors)
    {
        if (cnt[p] < c)
        {
            cout << "No"
                 << "\n";
            return;
        }
    }
    cout << "Yes"
         << "\n";
}

int main()
{
    std::cin.tie(nullptr);
    std::ios_base::sync_with_stdio(false);
    int kkt = 1;
    // cin >> kkt;
    while (kkt--)
    {
        solve();
    }
}
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