結果

問題 No.1731 Product of Subsequence
ユーザー ゆにぽけ
提出日時 2023-10-14 16:24:54
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 987 ms / 2,000 ms
コード長 3,697 bytes
コンパイル時間 1,433 ms
コンパイル使用メモリ 136,696 KB
最終ジャッジ日時 2025-02-17 07:48:29
ジャッジサーバーID
（参考情報） 		judge4 / judge5
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ファイルパターン 結果
sample AC * 4
other AC * 31
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 #
プレゼンテーションモードにする

#include<iostream>
#include<vector>
#include<algorithm>
#include<cstring>
#include<cassert>
#include<cmath>
#include<ctime>
#include<iomanip>
#include<numeric>
#include<stack>
#include<queue>
#include<map>
#include<unordered_map>
#include<set>
#include<unordered_set>
#include<bitset>
#include<random>
using namespace std;
template<int m> struct modint
{
    private:
    unsigned int value;
    static constexpr int mod() {return m;}
    public:
    constexpr modint(const long long x = 0) noexcept
    {
        long long y = x;
        if(y < 0 || y >= mod())
        {
            y %= mod();
            if(y < 0) y += mod();
        }
        value = (unsigned int)y;
    }
    constexpr unsigned int val() noexcept {return value;}
    constexpr modint &operator+=(const modint &other) noexcept
    {
        value += other.value;
        if(value >= mod()) value -= mod();
        return *this;
    }
    constexpr modint &operator-=(const modint &other) noexcept
    {
        unsigned int x = value;
        if(x < other.value) x += mod();
        x -= other.value;
        value = x;
        return *this;
    }
    constexpr modint &operator*=(const modint &other) noexcept
    {
        unsigned long long x = value;
        x *= other.value;
        value = (unsigned int) (x % mod());
        return *this;
    }
    constexpr modint &operator/=(const modint &other) noexcept
    {
        return *this *= other.inverse();
    }
    constexpr modint inverse() const noexcept
    {
        assert(value);
        long long a = value,b = mod(),x = 1,y = 0;
        while(b)
        {
            long long q = a/b;
            a -= q*b; swap(a,b);
            x -= q*y; swap(x,y);
        }
        return modint(x);
    }
    constexpr modint power(long long N) const noexcept
    {
        assert(N >= 0);
        modint p = *this,ret = 1;
        while(N)
        {
            if(N & 1) ret *= p;
            p *= p;
            N >>= 1;
        }
        return ret;
    }
    constexpr modint operator+() {return *this;}
    constexpr modint operator-() {return modint() - *this;}
    constexpr modint &operator++(int) noexcept {return *this += 1;}
    constexpr modint &operator--(int) noexcept {return *this -= 1;}
    friend modint operator+(const modint& lhs, const modint& rhs) {return modint(lhs) += rhs;}
    friend modint operator-(const modint& lhs, const modint& rhs) {return modint(lhs) -= rhs;}
    friend modint operator*(const modint& lhs, const modint& rhs) {return modint(lhs) *= rhs;}
    friend modint operator/(const modint& lhs, const modint& rhs) {return modint(lhs) /= rhs;}
    friend ostream &operator<<(ostream &os,const modint &x) {return os << x.value;}
};
//using mint = modint<998244353>;
using mint = modint<1000000007>;
long long gcd(long long a,long long b)
{
    while(b) {a %= b;swap(a,b);}
    return a;
}
#include<vector>
vector<pair<long long,int>> primefactorize(long long n)
{
    vector<pair<long long,int>> ret;
    for(long long p = 2;p*p <= n;p++)
    {
        if(n%p == 0)
        {
            int e = 0;
            while(n%p == 0) n /= p,e++;
            ret.push_back(make_pair(p,e));
        }
    }
    if(n > 1) ret.push_back(make_pair(n,1));
    return ret;
}
int N,K;
map<vector<int>,mint> dp[2];
void solve()
{
    cin >> N >> K;
    auto pf = primefactorize(K);
    int sz = (int)pf.size();
    int cur = 0;
    vector<int> s(sz,0);
    dp[cur][s] = 1;
    for(int i = 0;i < N;i++)
    {
        int nxt = 1-cur;
        dp[nxt].clear();
        long long A;
        cin >> A;
        A = gcd(A,K);
        vector<int> a(sz);
        for(int j = 0;j < sz;j++) while(A%pf[j].first == 0) A /= pf[j].first,a[j]++;
        for(auto it = dp[cur].begin();it != dp[cur].end();it++)
        {
            vector<int> V = it->first;
            dp[nxt][V] += it->second;
            for(int j = 0;j < sz;j++) V[j] += a[j],V[j] = min(V[j],pf[j].second);
            dp[nxt][V] += it->second;
        }
        swap(cur,nxt);
    }
    vector<int> g(sz);
    for(int i = 0;i < sz;i++) g[i] = pf[i].second;
    mint ans = dp[cur][g];
    if(K == 1) ans--;
    cout << ans << endl;
}
int main()
{
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int tt = 1;
    //cin >> tt;
    while(tt--) solve();
}
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