#include <algorithm>
#include <numeric>
#include <string>
#include <vector>
#include <iostream>
#include <queue>
#include <utility>
#include <cmath>
#include <map>
#include <unordered_map>
#include <functional>
using namespace std;

using ull = unsigned long long;

ull fast_pow(ull num,ull n)
{
    ull x = num;
    ull result = 1;
    while(n)
    {
        if(n & 1) result *= x;
        x *= x;
        n = n >> 1;
    }

    return result;
}

int main()
{
    ull n,k;
    cin >> n >> k;

    vector<ull> a(n);
    map<ull,vector<ull>> dic;

    for(int i =0; i < n; ++i)
    {
        cin >> a.at(i);
        ull tmp = a.at(i);

        int j = 2;
        while(j <= sqrt(a.at(i)))
        {
            if(tmp % j ==0)
            {
                vector<ull> t(n,0);
                tmp /= j;
                if(dic.find(j) != dic.end())
                {
                    dic.at(j).at(i) +=1;
                }
                else
                {
                    dic.emplace(j,t);
                    dic.at(j).at(i) = 1;
                }
            }
            else
            {
                ++j;
            }
        }

        vector<ull> t(n,0);
        if(dic.find(tmp) != dic.end())
        {
            dic.at(tmp).at(i) +=1;
        }
        else
        {
            dic.emplace(tmp,t);
            dic.at(tmp).at(i) = 1;
        }
    }

    ull sum = 1;
    for(auto&& x : dic)
    {
        sort(x.second.begin(),x.second.end(),greater<ull>());
        ull max_index = k > x.second.size() ? x.second.size() : k;
        ull count = 0;
        for(int i =0; i < k ; ++i)
        {
            count += x.second.at(i);
        }
        sum = (sum*fast_pow(x.first,count)) % static_cast<int>(1e9+7);
    }

    cout << sum << endl;
}