using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.IO;

class Iroha
{
    public Iroha() { }
    public static int Main()
    {
        new Iroha().calc();
        return 0;
    }

    Scanner cin;
    Dictionary<int, List<int>> dic;

    void GetDivisor(int a)
    {
        for (int i = 2; i * i <= a; i++)
        {
            if (a % i == 0)
            {
                int count = 0;
                while (a % i == 0)
                {
                    count++;
                    a /= i;
                }
                add(i, count);
            }
        }
        if (a != 0)
        {
            add(a, 1);
        }
    }

    void add(int a, int b)
    {
        if (!dic.ContainsKey(a)) dic[a] = new List<int>();
        dic[a].Add(b);
    }

    void calc()
    {
        cin = new Scanner();
        int N = cin.nextInt();
        int K = cin.nextInt();
        dic = new Dictionary<int, List<int>>();
        for (int i = 0; i < N; i++)
        {
            GetDivisor(cin.nextInt());
        }

        long ans = 1;
        long mod = 1000000007;

        foreach (var item in dic)
        {
            int a = item.Key;
            var b = item.Value;
            b.Sort();
            b.Reverse();
            for (int i = 0; i < Math.Min(b.Count, K); i++)
            {
                for (int j = 0; j < b[i]; j++)
                {
                    ans *= a;
                    ans %= mod;
                }
            }

        }

        Console.WriteLine(ans);
    }
    
}

class Scanner
{
    string[] s;
    int i;

    char[] cs = new char[] { ' ' };

    public Scanner()
    {
        s = new string[0];
        i = 0;
    }

    public string next()
    {
        if (i < s.Length) return s[i++];
        string st = Console.ReadLine();
        while (st == "") st = Console.ReadLine();
        s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        i = 0;
        return next();
    }

    public int nextInt()
    {
        return int.Parse(next());
    }

    public long nextLong()
    {
        return long.Parse(next());
    }

    public double nextDouble()
    {
        return double.Parse(next());
    }

}