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.
inputs = input()
lists= input()
inputs = inputs.split(' ')
lists = sorted(map(int,lists.split(' ')))
aux = [1]*len(lists)
count=0
center=int(len(lists)/2)
found = True

for i in range(len(lists)):
    center=int(len(lists)/2)
    if aux[i] == 1:
        count+=1
        while center>0 and center<len(lists) and lists[center]>(lists[i]) :
            if lists[center] <= lists[i]*2:
                if lists[i]*2 == lists[center]:
                    aux[center]=0
                    break
                center+=1
            elif lists[center] >= lists[i]*2:
                if lists[i]*2 == lists[center]:
                    aux[center]=0
                    break
                center-=1
    found = True
print(count)
