#include <iostream>
#include <vector>
#include <algorithm>
#include <map>
#include <queue>
#include <cstdio>
#include <ctime>
#include <assert.h>
#include <chrono>
#include <random>
#include <numeric>
#include <set>
using namespace std;
typedef long long int ll;
using ull = unsigned long long;

constexpr ll mod=1e9+7;

map<int,vector<int>> v;

ll mod_pow(ll a,ll b){
    a%=mod;
    if(b==0)return 1;
    if(b==1)return a;
    ll res=mod_pow(a,b/2)%mod;
    res*=res; res%=mod;
    if(b%2)res*=a;
    return res%mod;
}

int main(){
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    int n,k; cin >> n >> k;
    while(n--){
        int a; cin >> a;
        for(int i=2;i*i<=a;i++){
            if(a%i==0){
                int cnt=0;
                while(a%i==0){
                    a/=i;
                    cnt++;
                }
                v[i].push_back(cnt);
            }
        }
        if(a>1)v[a].push_back(1);
    }
    ll res=1;
    for(auto p:v){
        sort(p.second.rbegin(), p.second.rend());
        int cnt=0;
        for(int i=0;i<min(k,(int)(p.second.size()));i++){
            cnt+=p.second[i];
        }
        (res*=mod_pow(p.first,cnt))%=mod;
    }
    printf("%lld\n",res);
}