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.

def get(aa, b, n):
  ret = 1
  tmp=aa
  while b:
    if b&0x1:ret=ret*tmp%n
    tmp = tmp*tmp%n
    b >>=1
  return ret


n,x = [int(_) for _ in raw_input().split()]
s = [int(_) for _ in raw_input().split()]

MOD=1000000007 
ans=0

sum_ = sum(s)
sed = [sum_ - _ for _ in s]
a = [1] * len(sed)



while 1:
  l = min(sed)

  #for i in xrange(l):
  #  ans *= (x % MOD)
  #  ans %= MOD
  #ans *= get(x, l, MOD)
  if sum_ - l < 0:
    ans += sum_
    break
  else:
    ans += l
    sum_ -= l
  #ans %= MOD

  for i in xrange(len(sed)):
    sed[i] -= l

  remain = 0
  remove = []
  for i in xrange(len(sed)):
    if sed[i] == 0:
      remove.append(i)
      remain += a[i]

  for i in remove[::-1]:
    sed.pop(i)
    a.pop(i)

  ts = 0
  while remain % x == 0:
    ts += 1
    remain /= x

  if not ts:
    break

  sed.append(ts)
  a.append(remain)


print get(x, ans, MOD)
