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.*;

public class Main {
    static final int MOD = (int)1e9 + 7;
    long powerMod(long a, long b) {
        long ret = 1;
        for (; b > 0; b >>= 1, a = a * a % MOD) {
            if ((b & 1) == 1) {
                ret = ret * a % MOD;
            }
        }
        return ret;
    }
    void run() {
        InputReader in = new InputReader(System.in);
        int n = in.nextInt();
        int x = in.nextInt();
        long sum = 0;
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = in.nextInt();
            sum += a[i];
        }
        TreeMap<Long, Integer> map = new TreeMap<Long, Integer>();
        for (int i = 0; i < n; i++) {
            a[i] = sum - a[i];
            if (map.containsKey(a[i])) {
                map.put(a[i], map.get(a[i]) + 1);
            } else {
                map.put(a[i], 1);
            }
        }
        long result = 1;
        while (true) {
            Long key = map.firstEntry().getKey();
            Integer value = map.firstEntry().getValue();
            map.remove(map.firstKey());
            boolean flag = false;
            while (value % x == 0) {
                key = key + 1;
                value /= x;
                flag = true;
            }
            if (flag) {
                if (map.containsKey(key)) {
                    value += map.get(key);
                    map.remove(key);
                }
                map.put(key, value);
                continue;
            }
            long delta = Math.min(sum, key);
            result = powerMod(x, delta) % MOD;
            break;
        }
        PrintWriter out = new PrintWriter(System.out);
        out.println(result);
        out.close();
    }
    public static void main(String[] args) {
        new Main().run();
    }
}

class InputReader {
    BufferedReader buff;
    StringTokenizer tokenizer;
    InputReader(InputStream stream) {
        buff = new BufferedReader(new InputStreamReader(stream));
        tokenizer = null;
    }
    boolean hasNext() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(buff.readLine());
            } catch (Exception e) {
                return false;
            }
        }
        return true;
    }
    String next() {
        if (!hasNext()) {
            throw new RuntimeException();
        }
        return tokenizer.nextToken();
    }
    int nextInt() {
        return Integer.parseInt(next());
    }
}
