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 static java.lang.Integer.*;
import static java.lang.Math.*;

public class Problem359C4 {
    static BufferedReader in;
    static PrintWriter out;

    public static void main(String[] args) throws Exception {
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        new Problem359C4().go();
        out.close();
    }

    final long MOD = 1000000007;

    void go() throws IOException {
        String[] inp = in.readLine().split("\\s+");
        int n = parseInt(inp[0]);
        long x = parseInt(inp[1]);
        long[] a = new long[n];
        inp = in.readLine().split("\\s+");
        long powerSum = 0;
        for (int i = 0; i < n; i++) {
            a[i] = Long.parseLong(inp[i]);
            powerSum += a[i];
        }
        TreeMap<Long, Integer> powCounter = new TreeMap<Long, Integer>();
        long prevPow = powerSum - a[n - 1];
        int samePowCount = 0;
        for (int i = n - 1; i >= 0; i--) {
            long curPow = powerSum - a[i];
            if (curPow == prevPow) {
                samePowCount++;
            } else {
                updatePowCounter(powCounter, prevPow, samePowCount, x);
                prevPow = curPow;
                samePowCount = 1;
            }
        }
        updatePowCounter(powCounter, prevPow, samePowCount, x);
        boolean ok = true;
        while (ok && !powCounter.isEmpty()) {
            long leastPow = powCounter.firstKey();
            ok = updatePowCounter(powCounter, leastPow, 0, x);
        }
        long commonPow = powCounter.firstKey();
        out.println(calcPow(x, min(commonPow, powerSum)));
    }

    private long calcPow(long base, long exp) {
        long result = 1;
        base = base % MOD;
        while (exp != 0) {
            if ((exp & 1) == 1)
                result = (result * base) % MOD;
            exp >>= 1;
            base = (base * base) % MOD;
        }
        return result;
    }

    private boolean updatePowCounter(TreeMap<Long, Integer> powCounter,
            long prevPow, int samePowCount, long x) {

        Integer existingCount = powCounter.get(prevPow);
        int totalPowCount = samePowCount
                + (existingCount == null ? 0 : existingCount);
        int[] val = calcFactorCount(x, totalPowCount);

        long newPow = prevPow + val[0];
        if (newPow == prevPow) {
            powCounter.put(prevPow, totalPowCount);
            return false;
        }
        Integer existingNewPowCount = powCounter.get(newPow);
        int newPowCount = val[1]
                + (existingNewPowCount == null ? 0 : existingNewPowCount);

        powCounter.remove(prevPow);
        powCounter.put(newPow, newPowCount);
        return newPow != prevPow;
    }

    private int[] calcFactorCount(long x, int totalPowCount) {
        int[] ret = new int[2];
        int freq = 0;
        while (totalPowCount % x == 0) {
            totalPowCount /= x;
            freq++;
        }
        ret[0] = freq;
        ret[1] = totalPowCount;
        return ret;
    }
}