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 typing import List, Tuple

def bs(c: int, arr: List[int]) -> None:
    l, r = 0, len(arr) - 1
    while l <= r:
        m = (l + r) // 2
        if arr[m] == c:
            res[m] = 0
            return
        elif arr[m] < c:
            l = m + 1
        else:
            r = m - 1

def solve() -> None:
    n, k = map(int, input().split())
    arr = list(map(int, input().split()))
    arr.sort()
    ans = 0
    for i in range(n):
        if res[i]:
            bs(arr[i] * k, arr)
    for i in range(n):
        ans += res[i]
    print(ans)

M = 2 * 10**5 + 1
res = [1] * M
solve()
