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.
/*
Keep solving problems. 
*/
import java.util.*;
import java.io.*;

public class CFA {

    BufferedReader br;
    PrintWriter out;
    StringTokenizer st;
    boolean eof;
    final long MOD = 1000L * 1000L * 1000L + 7;
    int[] dx = {1, 2, 1, 1};
    int[] dy = {0, 0, -1, 1};

    void solve() throws IOException {
        int n = nextInt();
        long x = nextInt();
        int[] arr = nextIntArr(n);
        int max = 0;
        long sum = 0;
        for (int v : arr) {
            max = Math.max(max, v);
            sum += v;
        }

        Map<Integer, Long> hm = new HashMap<>();
        for (int i = 0; i < n; i++) {
            arr[i] = max - arr[i];
            hm.put(arr[i], hm.getOrDefault(arr[i], 0L) + 1);
        }

        sum -= max;
        int i = 0;
        while (true) {
            if (!hm.containsKey(i)) {
                i++;
                continue;
            }

            long cnt = hm.get(i);
            if (cnt % x != 0) {
                break;
            }

            hm.put(i + 1, hm.getOrDefault(i + 1, 0L) + cnt / x);
            i++;
        }

        sum += Math.min(i, max);
        long res = powMod(x, sum, MOD);
        out(res);
    }

    public long powMod(long N, long M, long MOD){//N^M % MOD
        if(M == 0L)
            return 1L;
        long[] hp = new long[64];
        boolean[] bp = new boolean[64];
        hp[0] = N;
        //hp[1] = N;
        for(int i = 1; i < hp.length; i++) {
            hp[i] = (hp[i - 1] * hp[i - 1]) % MOD;
        }
        for(int j = 0; j < hp.length; j++) {
            if((M & (1L << j)) != 0)
                bp[j] = true;
        }
        long res = 1;
        for(int i = 0;i < bp.length; i++){
            if(bp[i]) {
                res = (res * hp[i]) % MOD;
            }
        }
        return res;
    }

    void shuffle(int[] a) {
        int n = a.length;
        for(int i = 0; i < n; i++) {
            int r = i + (int) (Math.random() * (n - i));
            int tmp = a[i];
            a[i] = a[r];
            a[r] = tmp;
        }
    }

    long gcd(long a, long b) {
        while(a != 0 && b != 0) {
            long c = b;
            b = a % b;
            a = c;
        }
        return a + b;
    }

    private void outln(Object o) {
        out.println(o);
    }
    private void out(Object o) {
        out.print(o);
    }
    public CFA() throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        solve();
        out.close();
    }
    public static void main(String[] args) throws IOException {
        new CFA();
    }

    public long[] nextLongArr(int n) throws IOException{
        long[] res = new long[n];
        for(int i = 0; i < n; i++)
            res[i] = nextLong();
        return res;
    }
    public int[] nextIntArr(int n) throws IOException {
        int[] res = new int[n];
        for(int i = 0; i < n; i++)
            res[i] = nextInt();
        return res;
    }
    public String nextToken() {
        while (st == null || !st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                eof = true;
                return null;
            }
        }
        return st.nextToken();
    }
    public String nextString() {
        try {
            return br.readLine();
        } catch (IOException e) {
            eof = true;
            return null;
        }
    }
    public int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }
    public long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }
    public double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }
}

