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 sys
import typing
from os import path


def open_inputs():
    if path.exists("input.txt"):
        sys.stdin = open("input.txt", "r")
        sys.stdout = open("output.txt", "w")


def get_int(): return int(sys.stdin.readline().strip())


def get_ints(): return list(map(int, sys.stdin.readline().strip().split()))


def get_string(): return sys.stdin.readline().strip()


def printf(_s): sys.stdout.write(str(_s))


def binary_search(arr, x):
    low = 0
    high = len(arr) - 1

    while low <= high:

        mid = (high + low) // 2

        if arr[mid] < x:
            low = mid + 1

        elif arr[mid] > x:
            high = mid - 1

        else:
            return mid

    return None


def solve(array: typing.List[int], i, k):
    m = array[i] * k
    p = binary_search(array, m)
    if p:
        array.pop(p)
        s = len(array)
        if s > i + 1:
            solve(array, i + 1, k)
    return array


def main():
    open_inputs()

    n, k = get_ints()
    numbers = get_ints()

    numbers.sort()

    printf(len(solve(numbers, 0, k)))


if __name__ == '__main__':
    main()
