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}.
import sys
from math import *

def minp():
	return sys.stdin.readline().strip()

def mint():
	return int(minp())

def mints():
	return map(int, minp().split())

n, k = mints()
if k == 1:
	print(n)
	exit(0)
m = dict()
for i in mints():
	c = 0
	x = i
	while x % k == 0:
		x //= k
		c += 1
	if x not in m:
		m[x] = [0]*34
	m[x][c] += 1
r = 0
for i in m:
	f = True
	for j in m[i]:
		if f and j != 0:
			r += 1
			f = False
		else:
			f = True
print(r)
