Simon has a prime number x and an array of non-negative integers a1, a2, ..., an.

Simon loves fractions very much. Today he wrote out number <image> on a piece of paper. After Simon led all fractions to a common denominator and summed them up, he got a fraction: <image>, where number t equals xa1 + a2 + ... + an. Now Simon wants to reduce the resulting fraction. 

Help him, find the greatest common divisor of numbers s and t. As GCD can be rather large, print it as a remainder after dividing it by number 1000000007 (109 + 7).

Input

The first line contains two positive integers n and x (1 ≤ n ≤ 105, 2 ≤ x ≤ 109) — the size of the array and the prime number.

The second line contains n space-separated integers a1, a2, ..., an (0 ≤ a1 ≤ a2 ≤ ... ≤ an ≤ 109). 

Output

Print a single number — the answer to the problem modulo 1000000007 (109 + 7).

Examples

Input

2 2
2 2


Output

8


Input

3 3
1 2 3


Output

27


Input

2 2
29 29


Output

73741817


Input

4 5
0 0 0 0


Output

1

Note

In the first sample <image>. Thus, the answer to the problem is 8.

In the second sample, <image>. The answer to the problem is 27, as 351 = 13·27, 729 = 27·27.

In the third sample the answer to the problem is 1073741824 mod 1000000007 = 73741817.

In the fourth sample <image>. Thus, the answer to the problem is 1.
import java.util.*;
import java.io.*;
import static java.lang.Math.*;

public class PracticeProblem
{
    /*
     * This FastReader code is taken from GeeksForGeeks.com
     * https://www.geeksforgeeks.org/fast-io-in-java-in-competitive-programming/
     *
     * The article was written by Rishabh Mahrsee
     */
    public static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;

        public FastReader()
        {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt()
        {
            return Integer.parseInt(next());
        }

        long nextLong()
        {
            return Long.parseLong(next());
        }

        double nextDouble()
        {
            return Double.parseDouble(next());
        }

        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }

    public static FastReader in = new FastReader();
    public static PrintWriter out = new PrintWriter(System.out);
    public static final int MOD = (int)1e9 + 7;

    public static void main(String[] args)
    {
        solve();
        out.close();
    }
    private static void solve()
    {
        int n = in.nextInt(), x = in.nextInt();
        Map<Integer, Integer> counts = new TreeMap<>(Collections.reverseOrder());
        long sum = 0;

        for (int i = 0; i < n; i++)
        {
            int next = in.nextInt();
            sum += next;

            if (!counts.containsKey(next))
                counts.put(next, 0);

            counts.put(next, counts.get(next) + 1);
        }

        while (true)
        {
            int maxPower = counts.keySet().iterator().next();
            int amt = counts.get(maxPower);

            if (maxPower <= 0 || amt % x != 0)
            {
                out.println(power(x, max(0, sum - maxPower)));
                return;
            }

            counts.remove(maxPower);

            int cur = amt;
            int digit = 0;
            while (cur > 0)
            {
                if (cur % x != 0)
                {
                    if (!counts.containsKey(max(0, maxPower - digit)))
                        counts.put(max(0, maxPower - digit), 0);

                    counts.put(max(0, maxPower - digit), counts.get(max(0, maxPower - digit)) + (cur % x));
                }
                cur /= x;
                digit++;
            }
        }
    }

    private static long power(long a, long b)
    {
        long result = 1;
        for (; b > 0; a = a * a % MOD, b >>= 1)
            if ((b & 1) == 1)
                result = result * a % MOD;
        return result;
    }
}