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.

// Problem : C. Prime Number
// Contest : Codeforces Round #209 (Div. 2)
// URL : https://codeforces.com/contest/359/problem/C
// Memory Limit : 256 MB
// Time Limit : 1000 ms
// Powered by CP Editor (https://github.com/cpeditor/cpeditor)

import java.io.*;
import java.util.*;

public class a {

	public static void main(String[] args) {
		FastReader scan = new FastReader();
		PrintWriter out = new PrintWriter(System.out);
		Task solver = new Task();
		//int t = scan.nextInt();
		int t = 1;
		for(int i = 1; i <= t; i++) solver.solve(i, scan, out);
		out.close();
	}

	static class Task {

		public void solve(int testNumber, FastReader sc, PrintWriter pw) {
			int n  =sc.nextInt();
			int k = sc.nextInt();
			int[] arr= new int[n];
			long sum = 0;
			for(int i=0;i<n;i++){
				arr[i]=sc.nextInt();
				sum+=arr[i];
			}
			shuffle(arr);
			Arrays.sort(arr);
			HashMap<Integer,Integer> freq = new HashMap<>();
			Queue<Integer> q = new LinkedList<>();
			for(int i=n-1;i>=0;i--){
				q.add(arr[i]);
			}
			for(;!q.isEmpty();){
				int zz = q.poll();
				if(!freq.containsKey(zz)){
					freq.put(zz,0);
				}
				freq.put(zz,freq.get(zz)+1);
				if(freq.get(zz)>=k){
					freq.put(zz,0);
					q.add(zz-1);
				}
			}
			int max = 0;
			for(int x : freq.keySet()){
				if(freq.get(x)>0){
					max=Math.max(x,max);
				}
			}
			//pw.println(max);
			//pw.println((1l<<31)%1000000007);
			pw.println(binpow(k,sum-max,1000000007));
		}
		long binpow(long a, long b, long m) {
		    a %= m;
		    long res = 1;
		    while (b > 0) {
		        if ((b & 1)==1)
		            res = res * a % m;
		        a = a * a % m;
		        b >>= 1;
		    }
		    return res;
		}
	}

	static void shuffle(int[] a) {
		Random get = new Random();
		for (int i = 0; i < a.length; i++) {
			int r = get.nextInt(a.length);
			int temp = a[i];
			a[i] = a[r];
			a[r] = temp;
		}
	}

	static void shuffle(long[] a) {
		Random get = new Random();
		for (int i = 0; i < a.length; i++) {
			int r = get.nextInt(a.length);
			long temp = a[i];
			a[i] = a[r];
			a[r] = temp;
		}
	}

	static class FastReader {
		BufferedReader br;
		StringTokenizer st;

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

		public FastReader(String s) throws FileNotFoundException {
			br = new BufferedReader(new FileReader(new File(s)));
		}

		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	}

}