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())
l=list(map(int,input().split()))
l.sort()
d={}
c=1
p=[0]*n
d[l[0]]=0
p[0]=1
for i in range(1,n):
	a=c
	if l[i]%k==0 and (l[i]//k in d):
		a=d[l[i]//k]
		c-=1
	d[l[i]]=a
	p[a]+=1
	c+=1
s=0
for i in range(n):
	if p[i]==0:
		break
	s+=(p[i]//2)
	if p[i]%2!=0:
		s+=1
print(s)