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}.
def find(a, val):
    l = 0; r = len(a)
    while ((r - l)  > 1):
        m = (l+r) / 2
        if (a[m] < val):
            l = m
        else:
            r = m
    if (r < len(a)) and (a[r] == val):
        return r
    else:
        return len(a)


if __name__ == '__main__':
    n,k = map(int, raw_input().split())
    a = map(int, raw_input().split())
    a.sort()
    b = [True for _ in range(len(a)+1)]
    cnt = 0
    for i in range(len(a)):
        if b[i]:
            cnt += 1
            b[find(a,k*a[i])] = False
    print cnt
        
