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=[int(x) for x in input().split()]
arr=[int(x) for x in input().split()]
arr.sort()
d={}
for i in arr:
    if i%k==0 and i//k in d:
        d[i]=d[i//k]+1
        del d[i//k]
    else:
        d[i]=1
#print(d)
ans=0
for i in d:
    if d[i]%2:
        ans+=(d[i]//2)+1
    else:
        ans+=(d[i]//2)
print(ans)
    