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}.
n,k= map(int,input().split())
arr= list(map(int,input().split()))
arr.sort()
visited=[0]*n
i=0
group_2 = []
group_1 = []
while i<n:
    if visited[i]==0:
        group_1.append(arr[i])
        visited[i]=1
        x = arr[i]*k
        left=i
        right = n-1
        while left<=right:
            mid = left+(right-left)//2
            if arr[mid]==x:
                visited[mid]=1
                group_2.append(arr[mid])
                break
            elif arr[mid]<x:
                left=mid+1
            else:
                right=mid-1
        i+=1
    else:
        i+=1
print (max(len(group_1),len(group_2)))
