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.
# -*- coding: utf-8 -*-
import math
import sys
from collections import defaultdict
import collections
import heapq


class Solver(object):

    def fpow(self, n, i, m):
        res = 1
        x = n
        while i != 0:
            if i & 0x1 != 0:
                res = (res * x) % m
            i >>= 1
            x = (x*x) % m
        return res % m

    def run(self):
        n, x = readarray(int)
        a = readarray(int)

        suma = sum(a)
        degree = map(lambda x: suma-x, a)
        heapq.heapify(degree)

        prev = heapq.heappop(degree)
        count = 1
        while degree:

            head = heapq.heappop(degree)

            if prev != head:
                if count % x == 0:
                    for i in xrange(count/x):
                        heapq.heappush(degree, prev+1)
                    count = 1
                else:
                    break
            else:
                count += 1

            if count % x == 0:
                heapq.heappush(degree, head + 1)
                count = 0

            prev = head

        print(self.fpow(x, min(suma, prev), int(1e9+7)))


################################################################################
# ここからは見ちゃダメ！

def read(foo):
    return foo(raw_input())
def readarray(foo):
    return [foo(x) for x in raw_input().split()]
def dbg(a):
    sys.stderr.write(str(a))
def dbgln(a):
    sys.stderr.write(str(a) + "\n")

if __name__ == '__main__':
    Solver().run()
