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.InputStreamReader;
import java.util.Arrays;
import java.util.Comparator;
import java.util.HashMap;
import java.util.Map.Entry;
import java.util.StringTokenizer;

public class C {
	public static void main(String[] args) throws Exception {
		HashMap<Long, Integer> map = new HashMap<>();
		int n = nextInt();
		int x = nextInt();
		long sum = 0;
		int[] ar = new int[n];
		for (int i = 0; i < n; i++) {
			ar[i] = nextInt();
			sum += ar[i];
		}
		for (int i = 0; i < n; i++) {
			long toAdd = sum - ar[i];
			if (map.containsKey(toAdd)) {
				map.put(toAdd, map.get(toAdd) + 1);
			} else {
				map.put(toAdd, 1);
			}
		}
		Entry<Long, Integer>[] entries = new Entry[map.size()];
		entries = map.entrySet().toArray(entries);
		Arrays.sort(entries, new Comparator<Entry<Long, Integer>>() {

			@Override
			public int compare(Entry<Long, Integer> arg0,
					Entry<Long, Integer> arg1) {
				return arg0.getKey().compareTo(arg1.getKey());
			}
		});
		long min = -1;
		for (int i = 0; i < entries.length; i++) {
			min = entries[i].getKey();
			int cnt = entries[i].getValue();
			if (cnt % x==0) {
				long tmp = min+1;
				cnt/=x;
				while (cnt % x==0 && !map.containsKey(tmp)) {
					tmp++;
					cnt /= x;
				}
				if (map.containsKey(tmp)) {
					entries[i + 1].setValue(entries[i + 1].getValue() + cnt);
				} else {
					min = tmp;
					break;
				}
			} else {
				break;
			}
		}
		min=Math.min(min,sum);
		long mod = (long) (1e9 + 7);
		long res = 1;
		long base = x;
		while (min > 0) {
			if ((min & 1) == 1) {
				res = (res * base) % mod;
			}
			min >>= 1;
			base = (base * base) % mod;
		}
		System.out.println(res);
	}

	static BufferedReader br = new BufferedReader(new InputStreamReader(
			System.in));
	static StringTokenizer tokenizer = new StringTokenizer("");

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

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

	static String next() throws Exception {
		while (true) {
			if (tokenizer.hasMoreTokens()) {
				return tokenizer.nextToken();
			}
			String s = br.readLine();
			if (s == null) {
				return null;
			}
			tokenizer = new StringTokenizer(s);
		}
	}
}
