using System;
using System.Collections;
using System.Collections.Generic;
using System.Collections.Specialized;
using System.Text;
using System.Text.RegularExpressions;
using System.Linq;

class Program
{
    static void Main()
    {
        new Magatro().Solve();
    }
}

struct P
{
    public int Cost, Index;
    public P(int cost, int index)
    {
        Cost = cost;
        Index = index;
    }
}

class Magatro
{
    private int N, K;
    private int[] A;
    private List<int> Primes = new List<int>();
    private long ans = 1;
    private const int Mod = 1000000007;

    private void Scan()
    {
        var line = Console.ReadLine().Split(' ');
        N = int.Parse(line[0]);
        K = int.Parse(line[1]);
        A = new int[N];
        line = Console.ReadLine().Split(' ');
        for (int i = 0; i < N; i++)
        {
            A[i] = int.Parse(line[i]);
        }
    }

    private void P()
    {
        int max = 100000;
        bool[] b = new bool[max + 1];
        b[0] = true;
        b[1] = true;
        for (int i = 2; i * i <= max; i++)
        {
            if (!b[i])
            {
                for (int j = i + i; j <= max; j += i)
                {
                    b[j] = true;
                }
            }
        }
        for (int i = 0; i <= max; i++)
        {
            if (!b[i])
            {
                Primes.Add(i);
            }
        }
    }

    private void Calc(int n)
    {
        int c = 0;
        int[] cnt = new int[N];
        for (int i = 0; i < N; i++)
        {
            while (A[i] % n == 0)
            {
                A[i] /= n;
                cnt[i]++;
            }
        }
        Array.Sort(cnt, (a, b) => -a.CompareTo(b));
        for (int i = 0; i < K; i++)
        {
            c += cnt[i];
        }
        ans *= Pow(n, c);
        ans %= Mod;
    }

    private long Pow(long a, long b)
    {
        long res = 1;
        while (b > 0)
        {
            if (b % 2 == 1)
            {
                res *= a;
                res %= Mod;
            }
            b /= 2;
            a *= a;
            a %= Mod;
        }
        return res;
    }

    public void Solve()
    {
        Scan();
        P();
        foreach (int i in Primes)
        {
            Calc(i);
        }
        foreach (int i in A)
        {
            ans *= i;
            ans %= Mod;
        }
        Console.WriteLine(ans);
    }
}