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* &lt; *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.
The first line of the input contains two integers *n* and *k* (1 ≤ *n* ≤ 10<sup class="upper-index">5</sup>, 1 ≤ *k* ≤ 10<sup class="upper-index">9</sup>). The next line contains a list of *n* distinct positive integers *a*<sub class="lower-index">1</sub>, *a*<sub class="lower-index">2</sub>, ..., *a*<sub class="lower-index">*n*</sub> (1 ≤ *a*<sub class="lower-index">*i*</sub> ≤ 10<sup class="upper-index">9</sup>).

All the numbers in the lines are separated by single spaces.
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 = list(counts.keys())

for key in keys:
    if key in counts:
        if key*2 in counts:
            bin2 += counts[key*2]
            counts.pop(2*key)
        bin1 += counts[key]
        counts.pop(key)

print(max(bin1, bin2))
    