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}.
def search(v,l,n):
	low=0
	hi=n-1
	while(low<=hi):
		mid= low + (hi-low)//2
		if(l[mid]>v):
			hi=mid-1
		elif l[mid]<v:
			low=mid+1
		else:
			return mid
	return -1

n,k = map(int,input().strip().split())
v = list(map(int,input().strip().split()))
kmult = [False]*n
if(k==1): 
	print(n)
	quit()
c=n
v.sort()
hi=n
for j in range(n-1,-1,-1):
	i=v[j]
	if not kmult[j] and i%k==0:
		pos = search(i//k,v,hi)
		if pos>=0:
			kmult[pos]=True
			c-=1
			hi=pos
print(c)


			    			   			  	 	  		   	