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.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.StringTokenizer;

public class C {
	static BufferedReader in;
	static StringTokenizer st;
	static PrintWriter out;
	public static void main(String[] args) throws IOException {
		begin();
		solve();
		end();
	}
	private static void end() {
		out.close();
	}
	private static void solve() throws IOException {
		int n = nextInt();
		int x = nextInt();
		long sum = 0;
		long []arr = new long [n];
		for (int i = 0; i < arr.length; i++) {
			arr[i] = nextLong();
			sum += arr[i];
		}
		long []a = new long [n];
		for (int i = 0; i < arr.length; i++) {
			a[i] = (sum-arr[i]);
		}
		Arrays.sort(a);
		long pow = a[0];
		int cnt = 0;
		for (int i = 0; i < a.length; i++) {
			while (cnt % x == 0 && pow != a[i]){
				cnt /= x;
				pow++;
			}
			if (a[i] == pow) cnt++;
			else break;
		}
		while (cnt > 0 && cnt % x == 0){
			pow++;
			cnt /= x;
		}
		pow = Math.min(pow, sum);
		BigInteger b = new BigInteger(x+"");
		write(b.modPow(new BigInteger(pow+""), new BigInteger("1000000007")));
	}
	private static long nextLong() throws  IOException {
		return Long.parseLong(next());
	}
	private static void writeln(Object t) {
		out.println(t);
	}
	private static void write(Object t) {
		out.print(t);
	}
	private static int nextInt() throws  IOException {
		return Integer.parseInt(next());
	}
	private static String next() throws IOException {
		while (!st.hasMoreElements())
			st = new StringTokenizer(in.readLine());
		
		return st.nextToken();
	}
	private static void begin() {
		out = new PrintWriter(new OutputStreamWriter(System.out));
		st = new StringTokenizer("");
		in = new BufferedReader(new InputStreamReader(System.in));
	}

}
