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}.
# %matplotlib inline

def main():
    n, k = [int(x) for x in input().split(' ')]
    if k==1:
        print(n)
        return
    a = []
    b = {}
    a = [int(x) for x in input().split(' ')]
    a.sort()

    c=dict(zip(a,range(n)))
    a=c
    count = {}

    for x in a:
        if x % k == 0 and int(x / k) in a:
            b[x] = b[int(x / k)]
            count[b[int(x / k)]] += 1
        else:
            b[x] = x
            count[x] = 1

    for x,y in count.items():
        n -= int(y / 2)

    print(n)


main()
