#include<iostream>
#include<algorithm>
#include<vector>
#include<string>
#include<utility>
#include<map>
#include<set>
#include<queue>
#include<stack>
#include<functional>
#include<math.h>
#include<random>
#include <bitset>
using namespace std;
#define N (1000000000+7)
//#define N 998244353
#define INF 1e16
typedef long long ll;
typedef pair<int,int> P;
typedef pair<int,P> Q;

const int inf = (int)1e9; 

ll gcd(ll a, ll b) {
	if (b > a) {
		ll tmp = b;
		b = a;
		a = tmp;
	}
	if (a%b == 0)return b;
	else return gcd(b, a%b);
}


ll inv(ll x,ll power) {
	ll res = 1;
	ll k = power;
	ll y = x%N;
	while (k) {
		if (k & 1)res = (res*y) % N;
		y = (y%N*y%N) % N;
		k /= 2;
	}
	return res;
}

int main(void){
	ll n,k;
	cin>>n>>k;
	map<ll,vector<ll>>mp;
	set<ll>s;
	for(int i=0;i<n;i++){
		ll a;
		cin>>a;
		ll t=a;
		for(ll j=2;j*j<=a;j++){
			if(t%j==0){
				ll num = 0;
				while(t%j==0){
					t/=j;
					num++;
				}
				s.insert(j);
				mp[j].push_back(num);
			}
		}
		if(t>1){
			mp[t].push_back(1);
			s.insert(t);
		}
	}
	ll ans = 1;
	for(auto itr = s.begin();itr!=s.end();++itr){
		ll p = *itr;
		sort(mp[p].rbegin(),mp[p].rend());
		ll m = 0;
		ll len = min(k,(ll)mp[p].size());
		for(int i=0;i<len;i++)m+=mp[p][i];
		ll tmp = inv(p,m);
		ans = (ans*tmp)%N;
	}
	cout<<ans<<endl;
	return 0;
}