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())
lis = [0]+sorted(map(int,input().split()))
kk=lis[:]
ans=0
#print(lis)
for i in range(n,-1,-1):
    l=0
    r=i
    if kk[i]==0:
        continue
    while l<=r:
        mid = l + (r-l)//2
        if lis[i]/k <lis[mid]:
            r=mid-1
        else:
            l=mid+1         
    if lis[r]*10 ==lis[i]/k *10:
        kk[r]=0
    ans+=1
#    print(r,ans,lis[i],lis[r],lis[i]/k,lis)    
print(ans)        


