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 binarySearch(arr,x,left,right):
    if left > right:
        return False
    mid = (left+right)/2
    if arr[mid] > x:
        return binarySearch(arr,x,left,mid-1)
    elif arr[mid] < x:
        return binarySearch(arr,x,mid+1,right)
    else:
        return True
    
n,k = map(int,raw_input().split())

A = map(int,raw_input().split())
A.sort()
ansList = []
ans = 1
ansList.append(A[0])
i = 1
while i < n:
    if A[i]%k == 0:
        if not binarySearch(ansList,A[i]/k,0,ans-1):
            ansList.append(A[i])
            ans += 1
    else:
        ansList.append(A[i])
        ans += 1
    i += 1
print ans

