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 = input().split()
n = int(n); k = int(k)

a = [int(i) for i in input().split()]
a.sort()
mul = [0]*n
def search(a, val, k):
	l = 0; r = len(a)-1
	while l <= r:
		mid = (l+r)//2
		if a[mid] == val*k:
			return mid
		elif a[mid] > val*k:
			r = mid - 1
		else:
			l = mid + 1
	return -1

if n == 1:
	print(1)
else:
	count = 0
	for i in range(n):
		pos = search(a, a[i], k)
		if pos != -1 and pos != i:
			mul[pos] = mul[i] + 1
	# print(mul)
	for i in range(n):
		if not mul[i]%2:
			count += 1
	print(count)
