#include <iostream>
#include <vector>
#include <cstdio>
#include <sstream>
#include <map>
#include <string>
#include <algorithm>
#include <queue>
#include <cmath>
#include <functional>
#include <set>
#include <ctime>
#include <random>
#include <chrono>
#include <cassert>
using namespace std;

namespace {
	using Integer = long long; //__int128;
	template<class T> istream& operator >> (istream& is, vector<T>& vec){for(T& val: vec) is >> val; return is;}
	template<class T> istream& operator ,  (istream& is, T& val){ return is >> val;}
	template<class T> ostream& operator << (ostream& os, const vector<T>& vec){for(int i=0; i<vec.size(); i++) os << vec[i] << (i==vec.size()-1?"":" "); return os;}
	template<class T> ostream& operator ,  (ostream& os, const T& val){ return os << " " << val;}

	template<class H> void print(const H& head){ cout << head; }
	template<class H, class ... T> void print(const H& head, const T& ... tail){ cout << head << " "; print(tail...); }
	template<class ... T> void println(const T& ... values){ print(values...); cout << endl; }

	template<class H> void eprint(const H& head){ cerr << head; }
	template<class H, class ... T> void eprint(const H& head, const T& ... tail){ cerr << head << " "; eprint(tail...); }
	template<class ... T> void eprintln(const T& ... values){ eprint(values...); cerr << endl; }

	string operator "" _s (const char* str, size_t size){ return move(string(str)); }
	constexpr Integer my_pow(Integer x, Integer k, Integer z=1){return k==0 ? z : k==1 ? z*x : (k&1) ? my_pow(x*x,k>>1,z*x) : my_pow(x*x,k>>1,z);}
	constexpr Integer my_pow_mod(Integer x, Integer k, Integer M, Integer z=1){return k==0 ? z%M : k==1 ? z*x%M : (k&1) ? my_pow_mod(x*x%M,k>>1,M,z*x%M) : my_pow_mod(x*x%M,k>>1,M,z);}
	constexpr unsigned long long operator "" _ten (unsigned long long value){ return my_pow(10,value); }

	inline int k_bit(Integer x, int k){return (x>>k)&1;} //0-indexed

	mt19937 mt(chrono::duration_cast<chrono::nanoseconds>(chrono::steady_clock::now().time_since_epoch()).count());

	template<class T> string join(const vector<T>& v, const string& sep){
		stringstream ss; for(int i=0; i<v.size(); i++){ if(i>0) ss << sep; ss << v[i]; } return ss.str();
	}
}

constexpr long long mod = 9_ten + 7;

vector<pair<long long, long long> > prime_factorization(long long N){
	vector< pair<long long, long long> > ret;
	
	for(long long i=2; i*i<=N; i++){
		long long tmp = 0;
		while(N%i==0){
			tmp++;
			N/=i;
		}
		if(tmp>0){
			ret.push_back( make_pair(i, tmp) );
		}
	}
	if(N!=1){
		ret.push_back( make_pair(N, 1) );
	}
	return ret;
}


int main(){
	int n,k;
	cin >> n,k;
	vector<long long> a(n);
	cin >> a;

	map<long long, priority_queue<int, vector<int>, greater<int>> > m;
	for(int i=0; i<n; i++){
		auto p = prime_factorization(a[i]);
		for(auto x : p){
			m[x.first].push(x.second);
			while(m[x.first].size() > k) m[x.first].pop();
		}
	}

	long long ans = 1;
	for(auto& s : m){
		long long k = 0;
		while(s.second.size()){
			k += s.second.top();
			s.second.pop();
		}
		long long tmp = my_pow_mod(s.first, k, mod);
		ans = ans * tmp % mod;
	}

	
	println(ans);
	return 0;
}