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}.
n, k = map(int, input().split())

s = list(map(int, input().split()))

s = sorted(s)

my_dict = {}

for i in s:
	if i not in my_dict:
		my_dict[i] = 1

ans = {}
if k != 1:
	count = 0
	for i in my_dict:
		if i*k in my_dict and i not in ans:
			ans[i*k] = 1

print(len(my_dict)-len(ans))
		
