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

inp = sys.stdin.read().strip().splitlines()
n, k = [int(i) for i in inp[0].split(' ')]
a = [int(i) for i in inp[1].split(' ')]

a.sort()
aa = set(a)

if k > 1:
    for i in a:
        if i in aa and i*k in aa:
            aa.remove(i*k)

sys.stdout.write(str(len(aa)))
