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.ArrayList;
import java.util.Collections;


public class Main {
	
	public static int  product(int x, long a,int mod){
		long res = 1;
		long p = x;;
		while(a > 0){
			if(a %2 == 1)res = (res *p)%mod;
			p=(p*p)%mod;
			a/=2;
		}
		
		return (int)res;
	}
	
	public static void main(String[] args) throws IOException{
		//for(int i = 0; i < 100; i++)System.out.println(i + " " +product(2,i,1000000007));
		int mod = 1000000007;
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String line = br.readLine();
		String[] el = line.split(" ");
		int n = Integer.parseInt(el[0]);
		int x = Integer.parseInt(el[1]);
		line = br.readLine();
		el = line.split(" ");
		int a[] = new int[n];
		
		
		ArrayList<Long > b = new ArrayList<Long>();
		
		long sum = 0;
		for(int i = 0; i < n; i++){
			a[i] = Integer.parseInt(el[i]);
			sum+=a[i];
		}
		for(int i = 0; i < n; i++)b.add(-(sum-a[i]));
		Collections.sort(b);
		while(true){
			//System.out.println(b.toString());
			long v = b.get(b.size()-1);
			int cnt = 0;
			while(b.size() > 0 && b.get(b.size()-1) == v){
				cnt ++;;
				b.remove(b.size()-1);
			}
			
			if(cnt % x != 0){
				v = Math.min(-v,sum);
				System.out.println(product(x, v, mod));
				return;
			}else {
				
				cnt /= x;
				for(int i = 0; i < cnt; i++){
					b.add(v-1);
				}
			}
			
		}
		
		
		/*
		if(x == 1){
			System.out.println(1);
			return;
		}
		long sum = 0;
		for(int i = 0; i < n; i++){
			a[i] = Integer.parseInt(el[i]);
			sum+=a[i];
		}
		long min = sum-a[n-1];
		ArrayList<Long> S = new ArrayList<Long>();
		for(int i = 0; i < n; i++){
			S.add(sum-a[i]-min);
		}
		
		Collections.sort(S);
		
		int v = 0;
		while(S.size() > 0){
			long m = S.get(0);
			int exs = S.size();
			while(S.size() > 0 && m == S.get(0)){
				S.remove(0);
			}
			
			int q = (exs - S.size()) % x;
			if(q == 0){
				v++;
				long r = (exs - S.size())/ x;
				for(int k = 0; k <r; k++){
					S.add(0,(long)m+1);
				}
				
			}
			else break;
		}
		
		int p = product(x, min+v, mod);

		System.out.println(p);*/
	}
}
