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.InputStream;
import java.io.InputStreamReader;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.PriorityQueue;
import java.io.IOException;
import java.util.StringTokenizer;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskC solver = new TaskC();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskC {
    final long MOD = (long) 1e9 + 7;
    final int N = (int) 1e5;
    public void solve(int testNumber, InputReader in, PrintWriter out) {
        int n = in.nextInt(), m = in.nextInt();
        int a[] = new int[N];
        long sum = 0;
        for (int i = 0; i < n; i++) {
            a[i] = in.nextInt();
            sum += a[i];
        }
        PriorityQueue<Long> pe = new PriorityQueue<>();
        for (int i = 0; i < n; i++) {
            pe.add(sum - a[i]);
        }

        int size = 1;
        long cur = pe.poll();
        while((size % m == 0) || (pe.size() > 0 && pe.peek() == cur)) {
            while (pe.size() > 0 && pe.peek() == cur) {
                size++;
                pe.poll();
            }
            if (size % m == 0) {
                size /= m;
                cur++;
            }
        }

        out.print(fast_pow(m, Math.min(sum, cur)));
    }

    public long fast_pow(long x, long pow) {
        if (pow == 0) {
            return 1;
        }
        return (fast_pow((x * x) % MOD, pow / 2) * (pow % 2 == 0 ? 1 : x)) % MOD;
    }
}

class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream), 32768);
        tokenizer = null;
    }

    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

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

}

