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.IOException;
import java.io.InputStreamReader;
import java.util.InputMismatchException;
import java.util.TreeMap;
import java.io.PrintStream;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Reader;
import java.io.Writer;
import java.io.InputStream;

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

class TaskC {
    /////////////////////////////////////////////////////////////

    public void solve(int testNumber, FastScanner in, FastPrinter out) {
   int n=in.nextInt(),p=in.nextInt();
        int[] A=in.readIntArray(n);
        long sum=0;
        TreeMap<Integer,Integer> tm=new TreeMap<Integer, Integer>();
        for (int i = 0; i < n; i++) {
           sum+=A[i];
            if(tm.containsKey(A[i]))tm.put(A[i],tm.get(A[i])+1);
            else tm.put(A[i],1);
        }
    int ans=tm.lastKey();
        int chk=0;
        while(chk==0){
            chk=1;
            int k=tm.lastKey();
            ans=k;
            if(tm.get(k)%p==0){
                chk=0;
                int hh=tm.get(k);
                tm.remove(k);
                while(hh%p==0){
                    hh/=p;k--;
                }
                if(tm.containsKey(k))tm.put(k,tm.get(k)+hh);
                else tm.put(k,hh);

            }

        }
        ans=Math.max(0,ans);
        sum-=ans;

        long ret= modPow(p,sum);
        out.println(ret);

    }
    static long MOD=1000000007;
    static long modPow(long a, long pow) {
    		long res = 1;
    		while (pow > 0) {
    			if ((pow & 1) != 0) {
    				res = res * a % MOD;
    			}
    			pow >>= 1;
    			a = a * a % MOD;
    		}
    		return res;
    	}

}

class FastScanner extends BufferedReader {

    public FastScanner(InputStream is) {
        super(new InputStreamReader(is));
    }

    public int read() {
        try {
            int ret = super.read();
//            if (isEOF && ret < 0) {
//                throw new InputMismatchException();
//            }
//            isEOF = ret == -1;
            return ret;
        } catch (IOException e) {
            throw new InputMismatchException();
        }
    }

    static boolean isWhiteSpace(int c) {
        return c >= 0 && c <= 32;
    }

    public int nextInt() {
        int c = read();
        while (isWhiteSpace(c)) {
            c = read();
        }
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int ret = 0;
        while (c >= 0 && !isWhiteSpace(c)) {
            if (c < '0' || c > '9') {
                throw new NumberFormatException("digit expected " + (char) c
                        + " found");
            }
            ret = ret * 10 + c - '0';
            c = read();
        }
        return ret * sgn;
    }

    public String readLine() {
        try {
            return super.readLine();
        } catch (IOException e) {
            return null;
        }
    }

    public int[] readIntArray(int n) {
        int[] ret = new int[n];
        for (int i = 0; i < n; i++) {
            ret[i] = nextInt();
        }
        return ret;
    }

    }

class FastPrinter extends PrintWriter {

    public FastPrinter(OutputStream out) {
        super(out);
    }

    public FastPrinter(Writer out) {
        super(out);
    }


}

