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.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class Main {

    IIO io;

    Main(IIO io) {
        this.io = io;
    }

    public static void main(String[] args) throws IOException {

        ConsoleIO io = new ConsoleIO();
        Main m = new Main(io);
        m.solve();
        io.flush();

//        Tester test = new Tester();test.run();
    }

    public void solve() {
        long mod = 1000000007;
        int[] l = io.readIntArray();
        int n = l[0], x = l[1];
        if(x == 1){
            io.writeLine("1");
            return;
        }
        l = io.readIntArray();
        Arrays.sort(l);
        long s = 0;
        for (int v : l) s += v;
        long m = s - l[l.length - 1];
        long res = 1;
        long p = x;
        for (int i = 0; i < 62; i++, p = (p * p) % mod)
            if ((m & (1L << i)) > 0)
                res = (res * p) % mod;
        HashMap<Integer, Integer> nums = new HashMap<Integer, Integer>();
        for(int i = 0;i<l.length;i++) {
            if (nums.containsKey(l[i])) nums.put(l[i], nums.get(l[i]) + 1);
            else nums.put(l[i], 1);
        }
        int c = 0;
        int d = l[l.length-1];
        for(int q = l[l.length-1];q>=0 && d>0;) {
            if (nums.containsKey(q)) c += nums.get(q);
            if (c % x == 0) {
                c /= x;
                res = (res * x) % mod;
                q--;
                d--;
            }
            else break;
        }
        io.writeLine(Long.toString(res));
    }

}

class ConsoleIO extends BaseIO {
    BufferedReader br;
    PrintWriter out;
    public ConsoleIO(){
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
    }
    public void flush(){
        this.out.close();
    }
    public void writeLine(String s) {
        this.out.println(s);
    }
    public void writeInt(int a) {
        this.out.print(a);
        this.out.print(' ');
    }
    public void writeWord(String s){
        this.out.print(s);
    }
    public String readLine() {
        try {
            return br.readLine();
        }
        catch (Exception ex){
            return "";
        }
    }
    public int read(){
        try {
            return br.read();
        }
        catch (Exception ex){
            return -1;
        }
    }
}
abstract class BaseIO implements IIO {

    public long readLong() {
        return Long.parseLong(this.readLine());
    }

    public int readInt() {
        return Integer.parseInt(this.readLine());
    }

    public int[] readIntArray() {
        String line = this.readLine();
        String[] nums = line.split(" ");
        int[] res = new int[nums.length];
        for (int i = 0; i < nums.length; i++) {
            res[i] = Integer.parseInt(nums[i]);
        }
        return res;
    }
    public long[] readLongArray() {
        String line = this.readLine();
        String[] nums = line.split(" ");
        long[] res = new long[nums.length];
        for (int i = 0; i < nums.length; i++) {
            res[i] = Long.parseLong(nums[i]);
        }
        return res;
    }
}
interface IIO {
    void writeLine(String s);
    void writeInt(int a);
    void writeWord(String s);
    String readLine();
    long readLong();
    int readInt();
    int read();
    int[] readIntArray();
    long[] readLongArray();
}

