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 sys import stdin


def main():
    n, k = map(int, stdin.readline().split())
    ar = list(map(int, stdin.readline().split()))
    if k == 1:
        print(n)
    else:
        ar.sort()
        lk = set()
        check = {}
        for elm in ar:
            lk.add(elm)
            check[elm] = False
        ans = 0
        max_val = ar[-1]
        for i in range(n):
            if not check[ar[i]]:
                cnt = 0
                curr = ar[i]
                while curr <= max_val and curr in lk:
                    cnt += 1
                    check[curr] = True
                    curr = curr * k
                ans += (cnt // 2) + (cnt % 2)
        print(ans)


if __name__ == "__main__":
    main()
