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.*;
import java.io.*;
import java.math.BigInteger;

public class c359C {
	FastScanner in;
	PrintWriter out;

	final long inf = 2147483647;
	static long M = (long) 1e9 + 7;

	public void solve() throws IOException {
		int n = in.nextInt();
		long x = in.nextlong();
		long a[] = new long[n + 1];
		long sum = 0;
		for (int i = 0; i < n; i++) {
			a[i] = in.nextlong();
			sum += a[i];
		}
		long c = 1;
		long min = sum - a[n - 1];
		for (int i = n - 1; i >= 1; i--) {
			while (c % x == 0 && a[i] > a[i - 1]) {
				c = c / x;
				min++;
				a[i]--;
			}
			if (a[i] > a[i - 1]) {
				break;
			}
			if (a[i] == a[i - 1]) {
				c++;
			}
		}
		while (c % x == 0) {
			c /= x;
			min++;
		}
		if (min > sum) {
			min = sum;
		}
		if (n == 1) {
			out.print(1);
		} else {
			out.println((new BigInteger("" + x).modPow(
					new BigInteger("" + min), new BigInteger("1000000007"))));
		}
	}

	public void run() {
		try {
			in = new FastScanner();
			out = new PrintWriter(System.out);

			solve();

			out.close();
		} catch (IOException e) {
			e.printStackTrace();
		}
	}

	class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		FastScanner() {
			try {
				br = new BufferedReader(new InputStreamReader(System.in));
			} catch (Exception e) {
				e.printStackTrace();
			}
		}

		String next() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		long nextlong() {
			return Long.parseLong(next());
		}
	}

	public static void main(String[] args) {
		new c359C().run();
	}

}
