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.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.List;
import java.util.Scanner;

public class Main{
	
	
	static final int MOD = (int)1e9 + 7;
	public static void main(String[] args){
		
		Scanner scanner = new Scanner(System.in);
		int n = scanner.nextInt();
		long x = scanner.nextInt();
		int[] a = new int[n];
		long s = 0;
		for(int i = 0; i < n ; ++i) {
			a[i] = scanner.nextInt();
			s += a[i];
		}
		
		List<Long> deg = new ArrayList<>();
		for(int i = 0; i < n ; ++i) {
			deg.add(s - a[i]);
		}
		
		Collections.sort(deg, new Comparator<Long>() {

			@Override
			public int compare(Long o1, Long o2) {
				if(o1 > o2) return -1;
				return 1;
			}
		
		});
		while(true) {
			int count = 0;
			long d = deg.get(deg.size() - 1);
			while(deg.size() > 0 && deg.get(deg.size() - 1) == d) {
				++count;
				deg.remove(deg.size() - 1);
			}
			
			if(count % x != 0) {
				long min = Math.min(s, d);
				System.out.println(pow(x, min));
				return;
			}else {
				count /= x;
				for(int i = 0; i < count; ++i) {
					deg.add(d + 1);
				}
			}
		}
		
	}
	
	
	static long pow(long x, long n) {
		if(n == 0) return 1;
		if(n % 2 == 0) return pow((x * x) % MOD, n / 2);
		return (x * pow((x * x) % MOD, (n - 1) / 2)) % MOD;
	}
	
	
	
	

	
}
