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 binary_search(a, x):
    l, r = 0, len(a)
    pos = -1
    while r - l > 0:
        n = l + (r - l) // 2
        if a[n] == x:
            pos = n
            break
        elif a[n] > x:
            r = n
        else:
            l = n
        if r - l == 1:
            break
    return pos


n, k = [int(e) for e in input().split()]
a = sorted([int(e) for e in input().split()])
c = 1
for i in range(n - 1):
    if binary_search(a[i + 1:], k * a[i]) == -1:
        c = c + 1
print(c)
