#define _CRT_SECURE_NO_WARNINGS
#define _USE_MATH_DEFINES
#define  _SCL_SECURE_NO_WARNINGS
#include <stdio.h>
#include <algorithm>
#include <utility>
#include <functional>
#include <cstring>
#include <queue>
#include <stack>
#include <math.h>
#include <iterator>
#include <vector>
#include <string>
#include <set>
#include <math.h>
#include <iostream> 
#include<map>
#include <stdlib.h>
#include <list>
#include <typeinfo>
#include <list>
#include <set>
#include <cstdint>
#define MAX_MOD 1000000007
#define REP(i,n) for(int i = 0;i < n;++i)
using namespace std;
int sosuu_counter[110000][1000] = {};
map<int, int> hogee;
int main() {
	int n, k;
	scanf("%d%d", &n, &k);
	REP(i, n) {
		long long n;
		cin >> n;
		int cnt = 2;
		while (true) {
			if (n % cnt == 0) {
				sosuu_counter[cnt][i]++;
				n /= cnt;
			}
			else {
				cnt++;
				if (cnt > sqrt(n)) {
					hogee[n]++;
					goto ok;
				}
			}
		}
	ok:;
	}
	long long ans = 1;
	for (auto itr = hogee.begin();itr != hogee.end();++itr) {
		int a = itr->first;
		int b = itr->second;
		for (int i = 0;i < b&&i < k;++i) {
			ans = (ans * a)%MAX_MOD;
		}
	}
	for (int i = 2;i <= 100000;++i) {
		sort(sosuu_counter[i], sosuu_counter[i] + 1000,greater<int>());
		int counter = 0;
		for (int q = 0;q < k;++q) {
			counter += sosuu_counter[i][q];
		}
		for (int q = 0;q < counter;++q) {
			ans = (ans*i) % MAX_MOD;
		}
	}
	cout << ans % MAX_MOD << endl;
}