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}.
from collections import defaultdict

n,k=[int(i) for i in input().strip().split()]
l=[int(i) for i in input().strip().split()]
if(k==1):
    print(n)
else:
    l.sort()
    ndict=defaultdict(list)
    for x in l:
        i=x
        while(i%k==0):
            i=i/k
        ndict[i].append(x)
    ans=0
    for i in ndict.values():
        count=0
        while(count<len(i)):
            if(count==len(i)-1):
                ans+=1
                break
            if(i[count]*k!=i[count+1]):
                ans+=1
                count+=1
            else:
                ans+=1
                count+=2
    print(ans)