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.*;

public class Main {
    
    private static final long MOD = 1000000007;
    
    public static void main(String[] args) throws Exception {
        Scanner scan = new Scanner(System.in);
        
        int n = scan.nextInt();
        int x = scan.nextInt();
        // be care of Overflow!!!
        long[] arr = new long[n];
        read(scan, arr);
        
        long sum = 0;
        for (long val : arr) {
            sum += val;
        }
        
        for (int i = 0; i < n; i++) {
            arr[i] = sum - arr[i];
        }
        
        long r = arr[n - 1];
        int count = 1;
        int index = n - 2;
        while (true) {
            while (index >= 0 && arr[index] == r) {
                index--;
                count++;
            }
            if (index < 0) {
                break;
            }
            
            while (arr[index] > r && count % x == 0) {
                count /= x;
                r++;
            }
            if (arr[index] > r) {
                break;
            }
        }
        while (count % x == 0) {
            count /= x;
            r++;
        }
        if (r > sum) {
            r = sum;
        }
        System.out.println(pow(x, r));
        scan.close();
    }
    
    private static long pow(long base, long r) {
        if (r == 0) {
            return 1;
        }
        long half = pow(base, r / 2);
        long res = (half * half) % MOD;
        if (r % 2 != 0) {
            res = (res * base) % MOD;
        }
        return res;
    }
    
    private static void print(int[] arr) {
        System.out.print(arr[0]);
        for (int i = 1; i < arr.length; i++) {
            System.out.print(" ");
            System.out.print(arr[i]);
        }
        System.out.println();
    }
    
    private static void print(long[] arr) {
        System.out.print(arr[0]);
        for (int i = 1; i < arr.length; i++) {
            System.out.print(" ");
            System.out.print(arr[i]);
        }
        System.out.println();
    }
    
    private static void read(Scanner scan, int[]... arrs) {
        int len = arrs[0].length;
        for (int i = 0; i < len; i++) {
            for (int[] arr : arrs) {
                arr[i] = scan.nextInt();
            }
        }
    }
    
    private static void read(Scanner scan, long[]... arrs) {
        int len = arrs[0].length;
        for (int i = 0; i < len; i++) {
            for (long[] arr : arrs) {
                arr[i] = scan.nextLong();
            }
        }
    }
    
    private static void decreaseByOne(int[]... arrs) {
        for (int[] arr : arrs) {
            for (int i = 0; i < arr.length; i++) {
                arr[i] --;
            }
        }
    }
}
