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())
arr = list(map(int, input().split()))
lol = {}
flag = {}
arr.sort()

for x in arr:
	flag[x] = 1

ans = 0
for i in range(len(arr)):
	if arr[i] in lol:
		continue
	
	cur = arr[i]
	cnt = 0

	while cur <= 1000000000:
		lol[cur] = 1
		if cur in flag:
			cnt += 1
		else:
			break
		cur = cur * k
		if k == 1:
			break

	ans += (cnt + 1) // 2
print(ans)
