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, raw_input().strip().split(' '))
ais = sorted(map(int, raw_input().strip().split(' ')))
ai_dict = {ai: i for i, ai in enumerate(ais)}

if k == 1:
    print n
    exit()

was = [False for _ in xrange(n)]
total = 0

for i in xrange(n):
    if not was[i]:
        was[i] = True
        chain = 1
        curr = ais[i]
        while (curr * k) in ai_dict:
            curr *= k
            index = ai_dict[curr]
            was[index] = True
            chain += 1
        total += (chain + 1) / 2

print total