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}.
#! /Library/Frameworks/Python.framework/Versions/2.6/bin/python

inp = raw_input().split()

n = int(inp[0])
k = int(inp[1])

def countAbove(minElem,lookupSet):
	ans = 1
	if (minElem*k in lookupSet):
		ans += countAbove(minElem*k,lookupSet)
	return ans

if (k == 1):
	print n
else:
	inp = raw_input().split()
	a = [int(inp[i]) for i in range(n)]

	lookupA = set(a)

	ans = 0
	for elem in a:
		if ((elem % k == 0) and (elem/k in lookupA)):
			pass
		else:
			ans += (countAbove(elem,lookupA)+1)/2

	print ans


