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 check(cnt):
    s = set()
    for i in a:
        if i % k > 0:
            s.add(i)
        else:
            if not (i / k) in s:
                s.add(i)

    if len(s) >= cnt:
        return True

    return False

n, k = map(int, raw_input().split())
a = map(int, raw_input().split(' '))
a.sort()
l = 1
r = n

while l < r:
    md = (l + r) / 2
    if check(md):
        l = md + 1
    else:
        r = md

if check(l):
    print "%d\n" % l
else:
    print "%d\n" % (l - 1)
