#include <bits/stdc++.h>
#include <atcoder/all>
using namespace atcoder;
#define rep(i, n) for (int i = 0; i < (n); ++i)

using namespace std;
using P = pair<int, int>;
using mint = modint1000000007;

vector<P> factorize(int n) {
    vector<P> res;
    for (int i = 2; i*i <= n; ++i) {
        if (n%i != 0) continue;
        res.emplace_back(i, 0);
        while (n%i == 0) {
            n /= i;
            res.back().second++;
        }
    }
    if (n != 1) res.emplace_back(n, 1);
    return res;
}

int main() {
    int n, k;
    cin >> n >> k;
    
    map<int, vector<int>> mp;
    rep(i, n) {
        int a;
        cin >> a;
        auto fs = factorize(a);
        for (auto [p, x] : fs) mp[p].push_back(x); 
    }
    
    mint ans = 1;
    for (auto [p, xs] : mp) {
        auto d = xs;
        ranges::sort(d, greater<>());
        if (d.size() > k) d.resize(k);
        int cnt = 0;
        rep(i, d.size()) cnt += d[i]; 
        ans *= mint(p).pow(cnt);
    }
    
    cout << ans.val() << '\n';
    
    return 0;
}