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.*;
import java.util.*;
import java.math.*;

public class problem359C{
    public static void main(String[]args)throws IOException{
        BufferedReader x=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer(x.readLine());
        int n=Integer.parseInt(st.nextToken());
        String base=st.nextToken();
        int b=Integer.parseInt(base);
        st=new StringTokenizer(x.readLine());
        long sum=0;
        long[]arr=new long[n];
        for (int i=0; i<n; i++){
            long cur=Long.parseLong(st.nextToken());
            sum+=cur;
            arr[i]=cur;
        }
        for (int i=0; i<n; i++){
            arr[i]=sum-arr[i];
        }
        Arrays.sort(arr);
        long next=0;
        long cur=arr[0];
        long ans=0;
        boolean done=false;
        for (int i=0; i<n; i++){
            if (arr[i]==cur){
                next++;
            }else{
                if (next%b==0){
                    next=next/b;
                    if (arr[i]!=cur+1){
                        cur++;
                        i--;
                    }else{
                        cur=arr[i];
                        next++;
                    }
                }else{
                    //cur is what you want
                    ans=cur;
                    done=true;
                    break;
                }
            }
        }
        if (!done){
            ans=arr[n-1];
            while (next%b==0){
                next=next/b;
                ans++;
            }
        }
        if (ans==0)ans=cur;
        ans=Math.min(ans,sum);
        
        BigInteger exp=new BigInteger(Long.toString(ans));
        System.out.println(new BigInteger(base).modPow(exp, new BigInteger("1000000007")));
    }
}