結果

問題 No.2313 Product of Subsequence (hard)
ユーザー SnowBeenDiding
提出日時 2026-01-31 19:59:07
言語 C++23
(gcc 15.2.0 + boost 1.89.0)
結果
TLE  
実行時間 -
コード長 5,235 bytes
記録
記録タグの例:
初AC ショートコード 純ショートコード 純主流ショートコード 最速実行時間
コンパイル時間 9,253 ms
コンパイル使用メモリ 436,416 KB
実行使用メモリ 44,596 KB
最終ジャッジ日時 2026-01-31 19:59:28
合計ジャッジ時間 18,747 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
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ファイルパターン 結果
sample AC * 3
other AC * 10 TLE * 1 -- * 16
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 

#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>

#include <atcoder/all>
#define rep(i, a, b) for (ll i = (ll)(a); i < (ll)(b); i++)
using namespace atcoder;
using namespace std;

typedef long long ll;

using mint = modint998244353;

vector<ll> divisor(ll n) {
    auto mod_mul = [](ll a, ll b, ll mod) -> ll {
        return (__int128)a * b % mod;
    };

    auto mod_pow = [&](ll base, ll exp, ll mod) -> ll {
        ll result = 1;
        base %= mod;
        while (exp) {
            if (exp & 1) result = mod_mul(result, base, mod);
            base = mod_mul(base, base, mod);
            exp >>= 1;
        }
        return result;
    };

    auto is_prime = [&](ll num) -> bool {
        if (num < 2) return false;
        int smallPrimes[12] = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37};
        for (int p : smallPrimes) {
            if (num == p) return true;
            if (num % p == 0) return false;
        }
        ll d = num - 1;
        int s = 0;
        while ((d & 1) == 0) {
            d /= 2;
            s++;
        }
        ll testPrimes[7] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};
        for (ll a : testPrimes) {
            if (a % num == 0) continue;
            ll x = mod_pow(a, d, num);
            if (x == 1 || x == num - 1) continue;
            bool composite = true;
            for (int i = 0; i < s - 1; i++) {
                x = mod_mul(x, x, num);
                if (x == num - 1) {
                    composite = false;
                    break;
                }
            }
            if (composite) return false;
        }
        return true;
    };

    function<ll(ll)> pollard_rho;
    pollard_rho = [&](ll num) -> ll {
        if (num % 2 == 0) return 2;
        mt19937_64 rng(random_device{}());
        uniform_int_distribution<ll> dist(2, num - 2);
        ll x = dist(rng), y = x, c = dist(rng), d = 1;
        auto f = [&](ll x, ll c, ll mod) -> ll {
            return (mod_mul(x, x, mod) + c) % mod;
        };
        while (d == 1) {
            x = f(x, c, num);
            y = f(y, c, num);
            y = f(y, c, num);
            d = gcd(abs(x - y), num);
            if (d == num) return pollard_rho(num);
        }
        return d;
    };

    function<void(ll, vector<ll> &)> factorize;
    factorize = [&](ll num, vector<ll> &factors) {
        if (num == 1) return;
        if (is_prime(num)) {
            factors.push_back(num);
            return;
        }
        ll factor = pollard_rho(num);
        factorize(factor, factors);
        factorize(num / factor, factors);
    };

    vector<ll> factors;
    factorize(n, factors);
    sort(factors.begin(), factors.end());
    vector<pair<ll, int>> factorCounts;
    for (ll f : factors) {
        if (factorCounts.empty() || factorCounts.back().first != f)
            factorCounts.push_back({f, 1});
        else
            factorCounts.back().second++;
    }
    vector<ll> divisors;
    function<void(int, ll)> dfs = [&](int idx, ll current) {
        if (idx == factorCounts.size()) {
            divisors.push_back(current);
            return;
        }
        ll prime = factorCounts[idx].first;
        int exp = factorCounts[idx].second;
        for (int i = 0; i <= exp; i++) {
            dfs(idx + 1, current);
            current *= prime;
        }
    };
    dfs(0, 1);
    sort(divisors.begin(), divisors.end());
    return divisors;
}

struct Comb {
    vector<mint> fact, ifact;
    int MAX_COM;
    Comb() {}
    Comb(int n, int mod) {
        MAX_COM = n;
        init(mod, MAX_COM);
    }
    void init(long long MOD, long long MAX_COM) {
        int n = MAX_COM;
        assert(n < MOD);
        fact = vector<mint>(n + 1);
        ifact = vector<mint>(n + 1);
        fact[0] = 1;
        for (int i = 1; i <= n; ++i) fact[i] = fact[i - 1] * i;
        ifact[n] = fact[n].inv();
        for (int i = n; i >= 1; --i) ifact[i - 1] = ifact[i] * i;
    }
    mint operator()(long long n, long long k) {
        if (k < 0 || k > n) return 0;
        return fact[n] * ifact[k] * ifact[n - k];
    }
};
Comb comb(5000010, 998244353);

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
    int n = v.size();
    rep(i, 0, n) { os << v[i] << " \n"[i == n - 1]; }
    return os;
}

void solve() {
    ll n, k;
    cin >> n >> k;
    vector<ll> a(n);
    unordered_map<ll, int> ma, revd;
    rep(i, 0, n) {
        cin >> a[i];
        a[i] = gcd(a[i], k);
        ma[a[i]]++;
    }
    auto div = divisor(k);
    rep(i, 0, div.size()) { revd[div[i]] = i; }
    int d = div.size();
    vector<mint> dp(d);
    dp[0] = 1;
    rep(i, 0, d) {
        int cnt = ma[div[i]];
        vector<mint> ndp(d);
        rep(j, 0, d) {
            if (dp[j] == 0) continue;
            ll cur = div[j];
            for (int c = 0; c <= cnt; c++) {
                ndp[revd[cur]] += dp[j] * comb(cnt, c);
                cur *= div[i];
                cur = gcd(cur, k);
            }
        }
        dp = ndp;
    }
    cout << dp[d - 1].val() << "\n";
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(15);
    solve();
}
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