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}.
n, k = map(int, raw_input().split())

data = map(int, raw_input().split())

data.sort()


def bsearch(data, lo, hi, target):
    while lo <= hi:
        mid = lo + (hi - lo)/2

        if data[mid] == target:
            return True

        elif target < data[mid]:
            hi = mid -1
        else:
            lo = mid + 1
    return False


cnt = 0
myset = []

for i in xrange(len(data)):
    curr = data[i]
    if curr %k == 0:
        tar = curr/k
        if not bsearch(myset, 0, len(myset)-1, tar):
            myset.append(curr)
    else:
        myset.append(curr)

print len(myset)
