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.math.BigInteger;
import java.util.Arrays;
import java.util.Collections;
import java.util.LinkedList;
import java.util.Scanner;


public class Simon_209C {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
        Integer n = in.nextInt();
        Integer x = in.nextInt();
        Integer an[] = new Integer[n];
        long sum = 0;
        
        
        for(int i = 0; i < n; i++){
            an[i] = in.nextInt();
            sum += an[i];
        }
        LinkedList<Long> exp = new LinkedList<Long>();
        long sumn[] = new long[n];
        for(int i = 0; i < an.length; i++){
        	sumn[i] = sum - an[i];
        	exp.add(sum - an[i]);
        }
        Collections.sort(exp);
        
        while(!exp.isEmpty()){
        	long v = exp.peek();
        	int cnt = 0;
        	while(!exp.isEmpty() && exp.peek() == v){
        		cnt++;
        		exp.pop();
        	}
        	if(cnt % x == 0 && cnt > 0){
        		cnt /= x;
        		for(int i = 0; i < cnt; i++){
        			exp.push(v+1);
        		}
        	} else {
        		v = Math.min(v, sum);
        		System.out.println((new BigInteger(""+x).modPow(new BigInteger(""+v), new BigInteger("1000000007"))));
        		return;
        	}
        }
	}

}
