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.InputStreamReader;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Collections;
import java.util.LinkedList;
import java.util.StringTokenizer;

public class C_209 {
    static BufferedReader stdin = new BufferedReader(new InputStreamReader(System.in));
    static StringTokenizer st = new StringTokenizer("");

    public static void main(String[] args) throws Exception {
        int n = readInt();
        int x = readInt();
        int m = 1000000007;
        
        ArrayList<Integer> a = new ArrayList();
        long sum = 0;
        for(int i = 0; i < n; ++i) {
            a.add(readInt());
            sum += a.get(i);
        }
        
        LinkedList<Long> exp = new LinkedList();
        for(int i = 0; i < n; ++i)
            exp.add(sum - a.get(i));
        Collections.sort(exp);
        
        while(!exp.isEmpty()) {
            int count = 1;
            long e = exp.pop();
            while(!exp.isEmpty() && e == exp.peek()) {
                ++count;
                exp.pop();
            }
            if(count%x == 0) {
                for(int i = 0; i < count/x; ++i)
                    exp.push(e+1);
            } else {
                System.out.println(BigInteger.valueOf(x).modPow(BigInteger.valueOf(Math.min(e, sum)), BigInteger.valueOf(m)));
                exp.clear();
            }
        }
    }

    static String readString() throws Exception {
        while(!st.hasMoreTokens())
            st = new StringTokenizer(stdin.readLine());
        return st.nextToken();
    }

    static int readInt() throws Exception {
        return Integer.parseInt(readString());
    }
}