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.
def f(tar,l,k):
    l.sort()
    d={}
    for i in l:
        d[i]=1

    a=set()
    b=set()
    for i in l:
        u=i*k
        if i not in b and i not in a:
            if i in d:
                a.add(i)
                b.add(u)
            else:
                a.add(i)
                a.add(u)
    if len(a)>=tar or len(b)>=tar:
        return True
    else:
        return False

n,k=map(int,input().split())
l=list(map(int,input().split()))

low,high,ans=0,n,0
while(low<=high):
    mid=low+(high-low)//2
    x=f(mid,l,k)
    if x:
        ans=max(ans,mid)
        low=mid+1
    else:
        high=mid-1

print(ans)