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.Scanner;
import java.util.TreeMap;

public class Main {

	private static Scanner scanner = new Scanner(System.in);

	public static void main(String[] args) {
		int n = scanner.nextInt();
		int x = scanner.nextInt();

		long[] values = new long[n];
		solver(n, x, values);
	}

	private static void solver(int n, int x, long[] values) {
		long soma = 0;
		for (int i = 0; i < n; i++) {
			values[i] = scanner.nextInt();
			soma += values[i];
		}
		
		long[] diferencas = new long[n];
		for (int i = 0; i < n; i++) {
			diferencas[i] = soma - values[i];
		}
		
		Arrays.sort(diferencas);
		TreeMap<Long, Integer> digits = new TreeMap<Long, Integer>();
		for (long p : diferencas) {
			if (!digits.containsKey(p)) {
				digits.put(p, 0);
			}
			int d = digits.get(p);
			assert d < x;
			if (d == x - 1) {
				long q = p;
				while (digits.containsKey(q) && digits.get(q) == x - 1) {
					digits.remove(q++);
				}
				if (!digits.containsKey(q)) {
					digits.put(q, 0);
				}
				digits.put(q, digits.get(q) + 1);
			} else {
				digits.put(p, d + 1);
			}
		}

		long y = digits.firstKey();

		final int MAX = 1000000007;

		int result = 0;

		if (x % MAX == 0) {
			result = (Math.min(y, soma) == 0 ? 1 : 0);
		} else {
			int xp = x % MAX;
			int yp;
			if (y >= soma) {
				yp = (int) (soma % (MAX - 1));
			} else {
				yp = (int) (y % (MAX - 1));
			}
			result = modExponencial(xp, yp, MAX);
		}

		System.out.println(result);
	}

	private static int modExponencial(int a, int b, int n) {
		long result = 1;
		ArrayList<Integer> values = new ArrayList<Integer>();
		int value = b;
		while (value > 0) {
			values.add(value & 1);
			value = value >> 1;
		}
		for (int i = values.size() - 1; i >= 0; i--) {
			result = (result * result) % n;
			if (values.get(i) == 1) {
				result = (result * a) % n;
			}
		}

		return (int) result;
	}
}