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.*;

public class Main {
    public static void main(String[] args) throws IOException {
        FastScanner in = new FastScanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        new Main().run(in, out);
        out.close();
    }

    public static int mod = 1_000_000_007;

    void run(FastScanner in, PrintWriter out) {

        int N = in.nextInt();
        int p = in.nextInt();
        long[] a = new long[N];

        long psum = 0;
        for (int i = 0; i < N; i++) {
            a[i] = in.nextInt();
            psum += a[i];
        }

        TreeMap<Long, Long> tm = new TreeMap<>();
        for (int i = 0; i < N; i++) {
            tm.put(psum-a[i], tm.getOrDefault(psum-a[i], 0L) + 1);
        }

        long smallestpow = 0;
        while (true) {
            // System.out.println(Arrays.toString(tm.entrySet().toArray()));
            Map.Entry<Long, Long> firstEntry = tm.firstEntry();
            smallestpow = firstEntry.getKey();
            if (firstEntry.getValue()%p == 0) {

                long cnt = firstEntry.getValue()/p;
                long v = firstEntry.getKey();
                tm.put(v+1, tm.getOrDefault(v+1, 0L)+cnt);
                tm.remove(firstEntry.getKey());
            } else break;
        }

        smallestpow = Math.min(smallestpow, psum);
        out.println(exp(p, smallestpow, mod));

    }

    long exp(long x, long pow, int mod) {
        long ret = 1;
        while (pow > 0) {
            if ((pow&1) == 1) ret = (ret*x)%mod;
            x = (x*x)%mod;
            pow >>= 1;
        }
        return ret;

    }

    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(InputStream in) {
            br = new BufferedReader(new InputStreamReader(in));
            st = null;
        }

        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());
        }
    }
}
