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 sys
read = lambda: sys.stdin.readline().strip()
readi = lambda: map(int, read().split())
from collections import *

n, k = readi()
nums = list(readi())

bin1 = bin2 = 0
counts = defaultdict(int)
for i in nums: counts[i] += 1

keys = sorted(list(counts.keys()))

for key in keys:
    if key in counts:
        if key*k in counts:
            bin2 += counts[key*k]
            counts.pop(k*key)
        bin1 += counts[key]
        counts.pop(key)

print(max(bin1, bin2))
    