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}.
#!/usr/bin/env python
import sys

def iterative_solve(a, k):
	forbidden = set()
	count     = 0
	for start in xrange(len(a)):
		if a[start] not in forbidden:
			count += 1
			forbidden.add(a[start] * k)

	return count

def dp(a, k, start, forbidden):
	if start >= len(a):
		return 0

	if a[start] in forbidden:
		return dp(a, k, start + 1, forbidden)
	else:
		#count = dp(a, k, start + 1, forbidden)
		
		forbidden.add(a[start] * k)
		count = 1 + dp(a, k, start + 1, forbidden)
		forbidden.remove(a[start] * k)

		return count

if __name__ == '__main__':
	n, k = map(int, sys.stdin.readline().strip().split())
	a 	 = map(int, sys.stdin.readline().strip().split())

	a.sort()
	print iterative_solve(a, k)