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.util.Arrays;
import java.util.PriorityQueue;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.AbstractCollection;
import java.math.BigInteger;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author Mahmoud Aladdin
 */
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 {
    public void solve(int testNumber, InputReader jin, PrintWriter jout) {
        int n = jin.int32();
        long x = jin.int64();

        long tot = 0;
        long[] terms = new long[n];
        for(int i = 0; i < n; i++) {
            terms[i] = jin.int64();
            tot += terms[i];
        }
        Arrays.sort(terms);

        PriorityQueue<Long> que = new PriorityQueue<>();
        for(int i = 0; i < n; i++) {
            que.add(tot - terms[i]);
        }

        long pow = que.poll();
        long occ = 1;
        while(true) {
            Long next = que.poll();
            if(next != null && next == pow) {
                occ++;
            } else {
                if(occ % x == 0) {
                    if(next != null) que.add(next);
                    long toAdd = occ / x;
                    for(int i = 0; i < toAdd; i++) {
                        que.add(pow + 1);
                    }
                    pow++;
                    occ = 0;
                } else {
                    
                    long toPow = Math.min(pow, tot);
                    BigInteger biPow = BigInteger.valueOf(toPow);
                    BigInteger biMod = BigInteger.valueOf((long)1e9+7);
                    BigInteger biBas = BigInteger.valueOf(x);
                    
                    jout.println(biBas.modPow(biPow, biMod));
                    break;
                }
            }
            if(next == null && que.isEmpty())
                break;
        }

    }
}

class InputReader {
    private static final int bufferMaxLength = 1024;
    private InputStream in;
    private byte[] buffer;
    private int currentBufferSize;
    private int currentBufferTop;
    private static final String tokenizers = " \t\r\f\n";

    public InputReader(InputStream stream) {
        this.in = stream;
        buffer = new byte[bufferMaxLength];
        currentBufferSize = 0;
        currentBufferTop = 0;
    }

    private boolean refill() {
        try {
            this.currentBufferSize = this.in.read(this.buffer);
            this.currentBufferTop = 0;
        } catch(Exception e) {}
        return this.currentBufferSize > 0;
    }

    public String line() {
        StringBuffer tok = new StringBuffer();
        Byte first;
        while((first = readChar()) != null) {
            tok.append((char)first.byteValue());
            if((char)first.byteValue() == '\n')
                break;
        }
        return tok.toString();
    }

    public Byte readChar() {
        if(currentBufferTop < currentBufferSize) {
            return this.buffer[this.currentBufferTop++];
        } else {
            if(!this.refill()) {
                return null;
            } else {
                return readChar();
            }
        }
    }

    public String token()  {
        StringBuffer tok = new StringBuffer();
        Byte first;
        while((first = readChar()) != null && (tokenizers.indexOf((char) first.byteValue()) != -1));
        if(first == null) return null;
        tok.append((char)first.byteValue());
        while((first = readChar()) != null && (tokenizers.indexOf((char) first.byteValue()) == -1)) {
            tok.append((char)first.byteValue());
        }
        return tok.toString();
    }


    public String next() {
        return token();
    }

    public Integer int32() throws NumberFormatException {
        String tok = token();
        return tok == null? null : Integer.parseInt(tok);
    }

    public Long int64() throws NumberFormatException {
        String tok = token();
        return tok == null? null : Long.parseLong(tok);
    }
}

