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}.
first_multiple_input = input().rstrip().split()
 
n = int(first_multiple_input[0])
 
k = int(first_multiple_input[1])
element = list(map(int, input().rstrip().split()))
element.sort()
cross = set(element)
 
for i in element:
    if (i in cross ):
        if i*k in cross:
            cross.remove(i*k)

if k==1:
    print(len(element))
else:
    print(len(cross))