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.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.StringTokenizer;


public class C {

    static StringTokenizer st;
    static BufferedReader br;
    static PrintWriter pw;
    static class Que implements Comparable<Que> {
        long pow, koef;
        public int compareTo(Que arg0) {
            if (this.pow>arg0.pow)
                return 1;
            if (this.pow<arg0.pow)
                return -1;
            return 0;
        }
        public Que(long pow, long koef) {
            this.pow = pow;
            this.koef = koef;
        }
    }
    public static void main(String[] args) throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        int n = nextInt();
        int x = nextInt();
        int[]a = new int[n+1];
        long sum = 0;
        for (int i = 1; i <= n; i++) {
            a[i] = nextInt();
            sum += a[i];
        }
        Long[]pow = new Long[n+1];
        for (int i = 1; i <= n; i++) {
            pow[i] = sum-a[i];
        }
        Arrays.sort(pow, 1, n+1);
        long[] p = new long[n+1];
        for (int i = 1; i <= n; i++) {
            p[i] = pow[i].longValue();
        }
        long gcdpow = 0;
        PriorityQueue<Que> q = new PriorityQueue<Que>();
        for (int i = 1; i <= n; i++) {
            q.add(new Que(p[i], 1));
        }
        while (!q.isEmpty()) {
            long pp = q.peek().pow;
            long ss = q.poll().koef;
            while (!q.isEmpty() && q.peek().pow==pp) {
                ss += q.poll().koef;
            }
            gcdpow = pp;
            if (gcdpow > sum)
                break;
            if (ss % x != 0)
                break;
            q.add(new Que(pp+1, ss/x));
        }
        gcdpow = Math.min(gcdpow, sum);
        long ans = BigInteger.valueOf(x).modPow(BigInteger.valueOf(gcdpow), BigInteger.valueOf((long)(1e9+7))).longValue();
        System.out.println(ans);
        pw.close();
    }
    private static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }
    private static long nextLong() throws IOException {
        return Long.parseLong(next());
    }
    private static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }
    private static String next() throws IOException {
        while (st==null || !st.hasMoreTokens())
            st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }
}
