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 K_multiple(a, n, k) : 

	a.sort()

	s = set()
	
	for i in range(n) : 
		
		# Check if x/k is already present or not 
		if ((a[i] % k == 0 and
			a[i] // k not in s ) or a[i] % k != 0) : 
			s.add(a[i]) 
			
	print(len(s))

if __name__ == "__main__" : 

	n,k = input().split()
	n = int(n)
	k = int(k)	
	a = list(map(int,input().split()))

	K_multiple(a, n, k)
