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}.
from math import ceil
n2,k = map(int, input().split())
l = list(map(int, input().split()))
l = sorted(l)
d = {}
for i in l:
    d[i] = 1
if k == 1:
    print(len(d))
else:
    used = {}
    ans = 0
    for i in l:
        if i in used: continue
        n = i
        num = 0
        while n in d:
            if n in used: break
            used[n] = 1
            n *= k
            num += 1
        ans += num//2
        if num&1 > 0:
            ans += 1
    print(ans)
