#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef vector<int> vint;
typedef pair<int,int> pint;
typedef vector<pint> vpint;
#define rep(i,n) for(int i=0;i<(n);i++)
#define reps(i,f,n) for(int i=(f);i<(n);i++)
#define all(v) (v).begin(),(v).end()
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define chmax(a, b) a = (((a)<(b)) ? (b) : (a))
#define chmin(a, b) a = (((a)>(b)) ? (b) : (a))
const int MOD = 1e9 + 7;
const int INF = 1e9;

int main(void){
	int n, k; cin >> n >> k;
	map<int, vector<int> > m;

	rep(i, n){
		ll a; cin >> a;

		reps(j, 2, a / 2 + 1){
			int cnt = 0;
			while(a % j == 0){
				cnt++;
				a /= j;
			}
			if(cnt != 0){
				m[j].push_back(cnt);
			}
		}
		if(a != 1){//aが素数の時
			m[a].push_back(1);
		}
	}

	ll ans = 1;
	for(auto itr = m.begin(); itr != m.end(); ++itr){
		auto key = itr->first;
		auto v = itr->second;
		sort(all(v));
		reverse(all(v));

		int size = min(k, (int)v.size());
		rep(i, size){
			ans *= pow(key, v[i]);
			ans %= MOD;
		}
	}
	printf("%lld\n", ans % MOD);
	return 0;
}