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.PrintWriter;
import java.io.StreamTokenizer;
import java.util.*;
public class Main {
    static StreamTokenizer in = new StreamTokenizer(System.in);
    static int ni () throws Exception{
        in.nextToken();
        return (int)in.nval;
    }
    public static void main(String[] args) throws Exception {
        int n1 = ni();
        long p1 = ni();
        long[] l1 = new long[n1];
        long total = 0;
        for (int i = 0; i < n1; i++){
            l1[i] = ni();
            total += l1[i];
        }
        TreeMap<Long, Long> m1 = new TreeMap<>();
        for (int i = 0; i < n1; i++){
            add(total - l1[i], m1);
        }
        long ptr = total - l1[l1.length - 1];
        for (;;){
            long v1 = m1.get(ptr);
            if (v1 % p1 == 0){
                m1.remove(ptr);
            }
            if (v1 >= p1) add(ptr + 1l, m1, v1 / p1);
            
            Long next = m1.higherKey(ptr);
            if (next == null) break;
            ptr = next;
        }
//      px(m1);
        long minPow = m1.firstKey();
        out.println(pow(p1, Math.min(minPow, total)));
        out.flush();
    }
    static void px(Object ...objects){
        System.out.println(Arrays.deepToString(objects));
    }
    static PrintWriter out = new PrintWriter(System.out);
    
    static long MOD = 1_000_000_007;
    static long pow(long base, long pow){
        if (pow == 0) return 1l;
        if (pow == 1) return base % MOD;
        long half = pow(base, pow >> 1);
        half = half * half % MOD;
        if (pow % 2l == 1l){
            half *= base;
            half %= MOD;
        }
        return half;
    }
    static void add(long n1, TreeMap<Long, Long> m1){
        long old = m1.containsKey(n1) ? m1.get(n1) : 0;
        m1.put(n1, old + 1l);
    }
    static void add(long n1, TreeMap<Long, Long> m1, long val){
        long old = m1.containsKey(n1) ? m1.get(n1) : 0;
        if (old + val != 0) m1.put(n1, old + val);
    }
}
