#include <bits/stdc++.h>
using namespace std;

#define rep(i,n) for (int i=0;i<(n);i++)
#define rep2(i,a,b) for (int i=(a);i<(b);i++)
#define rrep(i,n) for (int i=(n)-1;i>=0;i--)
#define rrep2(i,a,b) for (int i=(b)-1;i>=(a);i--)
#define all(a) (a).begin(),(a).end()

typedef long long ll;
typedef pair<int, int> P;

const ll mod = 1e9 + 7;

ll powmod (ll a, ll p) {
	ll ret = 1;
	ll mul = a;
	for (; p > 0; p >>= 1, mul = (mul * mul) % mod) {
		if ((p & 1) == 1) ret = (ret * mul) % mod;
	}
	return ret;
}

map<ll, ll> primeFactorize(ll n) {
    map<ll, ll> res;
    for (ll i = 2; i * i <= n; ++i) {
        while (n % i == 0) {
            ++res[i];
            n /= i;
        }
    }
    if (n > 1) ++res[n];
    return res;
}

signed main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(0);

    ll N, K;
    cin >> N >> K;
    vector<ll> a(N);
    rep(i, N) cin >> a[i];

    // 各素因数について、指数を大きい順に記録
    map<ll, priority_queue<ll> > exponents;
    rep(i, N) {
        auto res = primeFactorize(a[i]);

        // cout << "primeFactorize " << a[i] << ":";
        // for (auto p : res) {
        //     cout << " " << p.first << "^" << p.second;
        // }
        // cout << endl;

        for (auto p : res) {
            exponents[p.first].push(p.second);
        }
    }

    // cout << "Exponents:" << endl;
    // for (auto p : exponents) {
    //     cout << p.first << ": ";
    //     auto que = p.second;
    //     while (!que.empty()) {
    //         auto x = que.top(); que.pop();
    //         cout << " " << x;
    //     }
    //     cout << endl;
    // }
    // cout << endl;

    ll ans = 1;
    for (auto p : exponents) {
        auto x = p.first;
        auto que = p.second;
		ll num = 0;
		rep(i, K) {
			if (que.empty()) break;
			num += que.top(); que.pop();
		}
        ans *= powmod(x, num);
        ans %= mod;
    }

    cout << ans << endl;

}