using System;
using System.IO;
using System.Collections.Generic;
using System.Globalization;
using System.Linq;
using System.Text;
using E = System.Linq.Enumerable;


partial class Solver
{
    IEnumerable<int> GetFactorPrimes(PrimeSet primes, int x)
    {
        var r = new List<int>();
        foreach (var p in primes)
        {
            if (p * p > x) break;
            if (x % p == 0)
            {
                r.Add(p);
                while (x % p == 0) x /= p;
            }
        }
        if (x > 1) r.Add(x);
        return r;
    }

    public void Run()
    {
        var N = ni();
        var K = ni();
        var a = ni(N);

        var primes = new PrimeSet(100000);
        var ps = a.SelectMany(x => GetFactorPrimes(primes, x)).Distinct().ToArray();
        long ans = 1;
        foreach (var p in ps)
        {
            var power = new List<int>();
            foreach (var x in a)
            {
                int pow = 0;
                var xx = x;
                while (xx % p == 0)
                {
                    xx /= p;
                    pow++;
                }
                if (pow > 0) power.Add(pow);
            }
            power.Sort();
            power.Reverse();

            var s = power.Take(K).Sum();
            for (int i = 0; i < s; i++)
            {
                ans = (ans * p) % 1000000007;
            }
        }
        cout.WriteLine(ans);
    }


}

public class PrimeSet : List<int>
{
    private readonly bool[] isPrime;

    public PrimeSet(int size)
        : base()
    {
        isPrime = Enumerable.Repeat(true, size).ToArray();
        Add(2);
        for (int i = 3; i <= size; i += 2)
        {
            if (!isPrime[i >> 1]) continue;
            Add(i);
            for (long j = (long)i * i; j <= size; j += i + i)
                isPrime[j >> 1] = false;
        }
    }

    public bool IsPrime(long x)
    {
        if (x == 2) return true;
        if (x <= 1 || x % 2 == 0) return false;
        return isPrime[x >> 1];
    }
}

// PREWRITEN CODE BEGINS FROM HERE
partial class Solver : Scanner
{
    public static void Main(string[] args)
    {
#if LOCAL
        new Solver(Console.In, Console.Out).Run();
#else
        Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
        new Solver(Console.In, Console.Out).Run();
        Console.Out.Flush();
#endif
    }

#pragma warning disable IDE0052
    private readonly TextReader cin;
    private readonly TextWriter cout;
#pragma warning restore IDE0052

    public Solver(TextReader reader, TextWriter writer)
        : base(reader)
    {
        this.cin = reader;
        this.cout = writer;
    }
    public Solver(string input, TextWriter writer)
        : this(new StringReader(input), writer)
    {
    }

#pragma warning disable IDE1006
#pragma warning disable IDE0051
    private int ni() { return NextInt(); }
    private int[] ni(int n) { return NextIntArray(n); }
    private long nl() { return NextLong(); }
    private long[] nl(int n) { return NextLongArray(n); }
    private double nd() { return NextDouble(); }
    private double[] nd(int n) { return NextDoubleArray(n); }
    private string ns() { return Next(); }
    private string[] ns(int n) { return NextArray(n); }
#pragma warning restore IDE1006
#pragma warning restore IDE0051
}

public static class LinqPadExtension
{
    static public T Dump<T>(this T obj)
    {
#if LOCAL
        return LINQPad.Extensions.Dump(obj);
#else
        return obj;
#endif
    }
}
public class Scanner
{
    private readonly TextReader Reader;
    private readonly Queue<string> TokenQueue = new Queue<string>();
    private readonly CultureInfo ci = CultureInfo.InvariantCulture;

    public Scanner()
        : this(Console.In)
    {
    }

    public Scanner(TextReader reader)
    {
        this.Reader = reader;
    }

    public int NextInt() { return int.Parse(Next(), ci); }
    public long NextLong() { return long.Parse(Next(), ci); }
    public double NextDouble() { return double.Parse(Next(), ci); }
    public string[] NextArray(int size)
    {
        var array = new string[size];
        for (int i = 0; i < size; i++) array[i] = Next();
        return array;
    }
    public int[] NextIntArray(int size)
    {
        var array = new int[size];
        for (int i = 0; i < size; i++) array[i] = NextInt();
        return array;
    }

    public long[] NextLongArray(int size)
    {
        var array = new long[size];
        for (int i = 0; i < size; i++) array[i] = NextLong();
        return array;
    }

    public double[] NextDoubleArray(int size)
    {
        var array = new double[size];
        for (int i = 0; i < size; i++) array[i] = NextDouble();
        return array;
    }

    public string Next()
    {
        if (TokenQueue.Count == 0)
        {
            if (!StockTokens()) throw new InvalidOperationException();
        }
        return TokenQueue.Dequeue();
    }

    public bool HasNext()
    {
        if (TokenQueue.Count > 0)
            return true;
        return StockTokens();
    }
    static readonly char[] _separator = new[] { ' ' };
    private bool StockTokens()
    {
        while (true)
        {
            var line = Reader.ReadLine();
            if (line == null) return false;
            var tokens = line.Split(_separator, StringSplitOptions.RemoveEmptyEntries);
            if (tokens.Length == 0) continue;
            foreach (var token in tokens)
                TokenQueue.Enqueue(token);
            return true;
        }
    }
}