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
rl = lambda: sys.stdin.readline()

n, k = [int(a) for a in rl().split()]
ar = [int(a) for a in rl().split()]
ar.sort()

s = set()
for a in ar:
	s.add(a)

visited = set()
if k > 1:
	rtn = len(ar)
	for a in ar:
		if a not in visited:
			visited.add(a)
			now = a
			nVisited = 1
			while now*k in s:
				visited.add(now*k)
				now = now*k
				nVisited += 1
			rtn -= nVisited/2

else:
	rtn = len(ar)
print rtn