A k-multiple free set is a set of integers where there is no pair of integers where one is equal to another integer multiplied by k. That is, there are no two integers x and y (x < y) from the set, such that y = x·k.

You're given a set of n distinct positive integers. Your task is to find the size of it's largest k-multiple free subset.

Input

The first line of the input contains two integers n and k (1 ≤ n ≤ 105, 1 ≤ k ≤ 109). The next line contains a list of n distinct positive integers a1, a2, ..., an (1 ≤ ai ≤ 109).

All the numbers in the lines are separated by single spaces.

Output

On the only line of the output print the size of the largest k-multiple free subset of {a1, a2, ..., an}.

Examples

Input

6 2
2 3 6 5 4 10


Output

3

Note

In the sample input one of the possible maximum 2-multiple free subsets is {4, 5, 6}.
def bb(A, item):
    """Implementa pesquisa binária iterativamente."""
    esquerda, direita = 0, len(A) - 1
    while esquerda <= direita:
        meio = (esquerda + direita) // 2
        if A[meio] == item:
            return meio
        elif A[meio] > item:
            direita = meio - 1
        elif A[meio] < item:
            esquerda = meio + 1
    return -1

n,k = map(int,input().split())
a = list(map(int,input().split()))
a.sort()
menores = []
maiores = []
for i in range(n):
  if bb(menores, a[i])==-1:
    if bb(maiores, a[i])==-1:
      menores.append(a[i])
      maiores.append(a[i]*k)
    else:
      continue
  
print(len(menores))