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.
n, x = map(int, input().split())
a = [int(x) for x in input().split()]
def solve(a, s):
  #print (a)
  a.append((-1, 0))
  a.sort()
  b = []
  for i in range(1, len(a)):
    if a[i][0] != a[i-1][0]:
      b.append(a[i])
    else:
      b[-1] = (a[i][0], b[-1][1] + a[i][1])
  for i in range(len(b)):
    t = b[i][1]
    cnt = 0
    while t%x == 0:
      t //= x
      cnt += 1
    b[i] = (b[i][0] + cnt, t)
  #print (b)
  z = min(min(b)[0], s)
  if z == 0:
    return 0
  return z + solve([(x[0]-z, x[1]) for x in b], s-z)
s = sum(a)
print(pow(x, solve([(s-x, 1) for x in a], s), 10**9+7))