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.util.Map.Entry;
import java.util.StringTokenizer;
import java.util.TreeMap;

public class C01_PrimeNumber {

    public static void main(String... args) throws IOException {
        MyScanner sc = new MyScanner();
        int n = sc.nextInt();
        int x = sc.nextInt();

        TreeMap<Long, Integer> map = new TreeMap<>();
        int[] nn = new int[n];

        long sum = 0;
        for (int i = 0; i < n; i++) {
            nn[i] = sc.nextInt();
            sum += nn[i];
        }

        for (int i = 0; i < n; i++) {
            long v = sum - nn[i];
            Integer exist;
            map.put(v, ((exist = map.get(v)) == null) ? 1 : (exist + 1));
        }

        while (true) {
            Entry<Long, Integer> e = map.pollFirstEntry();
            int count = e.getValue();
            if (count >= x && e.getKey() < sum) {
                long pow = x;
                int powNum = 1;
                while (pow <= count) {
                    pow *= x;
                    powNum++;
                }
                powNum--;
                pow /= x;
                count -= pow;
                if (count > 0){
                    map.put(e.getKey(), count);
                }

                long newPow = powNum + e.getKey();
                Integer ex;
                map.put(newPow, ((ex = map.get(newPow)) != null) ? ex + 1 : 1);
            } else {
                long exp = (e.getKey() <= sum)? e.getKey() : sum;
                System.out.println(powmod(x, exp, 1000000007));
                return;
            }
        }

    }

    public static int powmod(long x, long e, int mod) {
        long out = 1;
        while (e > 0) {
            if (e % 2 == 1) {
                out = (out * x) % mod;
            }
            x = (x*x) % mod;
            e >>= 1;
        }
        return (int) out;
    }

    static class MyScanner {

        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public String next() throws IOException {
            if (st == null || !st.hasMoreTokens()) {
                String line = br.readLine();
                st = new StringTokenizer(line);
            }
            return st.nextToken();
        }

        public int nextInt() throws IOException {
            String next = next();
            return Integer.parseInt(next);
        }
    }
}
