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 bSearch(x,li):
	l=0
	h=len(li)
	while(l<=h):
		m=(l+h)//2
		if(li[m]==x):
			return m
		elif(li[m]>x):
			h=m-1
		else:
			l=m+1
	return -1
n,k=map(int,input().split())
li=list(map(int,input().split()))
li.sort()
s=set()
for i in range(n):
	if(li[i]%k==0):
		z = bSearch(li[i]//k,li)
		if(z!=-1):
			if li[z] not in s:
				s.add(li[i])
		else:
			s.add(li[i])
	else:
		s.add(li[i])
print(len(s))
		
