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 math
import random 
from queue import Queue
import time 



def main(arr,k):

  set_arr=set(arr)
  max_val=max(arr)
  if k==1:
    return len(set_arr)
  f={}
  for e in arr:
    if e not in f:
      f[e]=0
    f[e]+=1
  ans=0
  for e in arr:
    if e in set_arr:


      new_arr=[] 
      start=e 

      while start<=max_val:
        if start in set_arr:
          set_arr.remove(start)
          new_arr.append(f[start])
        else:
          new_arr.append(0)

        start*=k
      dp=[[0 for j in range(2)] for i in range(len(new_arr))]
      dp[0][0]=0 
      dp[0][1]=new_arr[0]

      for i in range(1,len(dp)):
        for j in range(len(dp[0])):

          if j==0:
            dp[i][j]=max(dp[i-1][0],dp[i-1][1])
          else:
            dp[i][j]=new_arr[i]+dp[i-1][0]
      ans+=max(dp[-1])
  return ans 

  

n,k=list(map(int,input().split()))
arr=list(map(int,input().split()))
print(main(arr,k))