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}.
import bisect


n, k = map(int, input().split())
a = list(sorted(map(int, input().split())))

cnt = 0
for i in range(len(a)):
    if not a[i]:
        continue

    cnt += 1

    x = a[i] * k
    pos = bisect.bisect_left(a, x, lo=i + 1)
    if pos < len(a) and a[pos] == x:
        a[pos] = 0

print(cnt)
