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}.
from collections import Counter
from sets import Set

n, k = map(int, raw_input().split())

if k == 1:
	print n
else:
	A = map(int, raw_input().split())
	D = {}
	for a in A:
		if a in D:
			D[a] += 1
		else:
			D[a] = 1
	
	avoid = Set([])
	st = 0
	E = sorted(D.iteritems())
	for a, qty in E:
		if a in avoid:
			continue
		elif a * k not in D:
			st += 1
		else:
			l = [D[a]]
			m = [a]
			while a * k in D:
				l.append(D[a*k])
				m.append(a*k)
				a *= k
			st += max(sum(l[0::2]), sum(l[1::2]))
			for x in m:
				avoid.add(x)
	print st
