#pragma region GNUC
//以下を参考にした
//https://yukicoder.me/wiki/auto_vectorization
#ifdef __GNUC__
#pragma GCC optimize ("O3")
#pragma GCC target ("avx")
#endif
#pragma endregion

#define _USE_MATH_DEFINES

#include <iostream>
#include <iomanip>
#include <stdio.h>

#include <sstream>
#include <algorithm>
#include <cmath>

#include <string>
#include <cstring>
#include <vector>
#include <valarray>
//#include <array>//x C++ (G++ 4.6.4)

#include <queue>
#include <complex>
#include <set>
#include <map>
#include <stack>
#include <list>

#include <cassert>//assert();
#include <fstream>
#include <random>
/////////
#define REP(i, x, n) for(int i = x; i < n; ++i)
#define rep(i,n) REP(i,0,n)

/////////
typedef long long LL;
typedef long double LD;
typedef unsigned long long ULL;
#define PII pair<int,int>
/////////
using namespace::std;

// 最大公約数
template<class T>
inline T gcd(T a, T b){return b ? gcd(b, a % b) : a;}
//inline T gcd(T a, T b){return b == 0 ? a : gcd(b, a % b);}

// 最小公倍数
template<class T>
inline T lcm(T a, T b){return a / gcd(a, b) * b;}
//inline T lcm(T a, T b){return a * b / gcd(a, b);}
////////////////////////////////
LL mod = (LL)1e9+7;

LL powMod(LL p,int n){
	if( n == 0 ) return 1;
	LL ret = 1;
	LL mul = p%mod;
	while(n){
		if(n&1){
			ret = (ret*mul)%mod;
		}
		n >>= 1;
		mul = (mul*mul)%mod;
	}
	return ret;
}

void solve(){
	int N,K;
	cin >> N >> K;
	map<int,vector<int> > primeMap;

	for(int i=0;i<N;++i){
		int val;
		cin >> val;
		for(int i=2;i*i<=val;++i){
			if( val % i != 0 ) continue;
			int count = 0;
			while(val%i == 0){
				val /= i;
				++count;
			}
			primeMap[i].push_back(count);
		}
		if( val > 1 ){
			primeMap[val].push_back(1);
		}
	}
	map<int,vector<int> >::iterator itr,end;
	itr = primeMap.begin();
	end = primeMap.end();
	LL ans = 1;
	for(;itr!=end;++itr){
		vector<int>::iterator nitr,nend;
		nitr = itr->second.begin();
		nend = itr->second.end();
		sort(nitr,nend,greater<int>() );
		int count = 0;
		for(int i=0;nitr!=nend && i<K;++nitr,++i){
			count += *nitr;
		}
		ans = ( ans * powMod( itr->first, count) ) % mod;
	}
	cout << ans << endl;
}

signed main(void){
	std::cin.tie(0);
	std::ios::sync_with_stdio(false);
	//std::cout << std::fixed;//小数を10進数表示
	//cout << setprecision(16);//小数点以下の桁数を指定
	
	solve();
}