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.
from collections import defaultdict
import heapq
class Solution:
    def multipleFree(self, array, n, k):
        # TODO write an algorithm here
        multipleSet = set()
        answer = []
        heapq.heapify(array)
        while array:
            x = heapq.heappop(array)
            if x not in multipleSet:
                answer.append(x)
                multipleSet.add(x*k)
        return len(answer)
 
if __name__ == "__main__":
    solution = Solution()
    n, k = list(map(int, input().split()))
    array = list(map(int, input().split()))
    
    print(solution.multipleFree(array, n, k))
        