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 traceback
import math
from collections import defaultdict
from functools import lru_cache


def main():
    N, k = map(int, input().split())
    nums = list(map(int, input().split()))
    s = set(nums)
    g1, g2 = [], []
    done = set()
    for n in nums:
        if n in done:
            continue
        g1.append(n)
        if n*k in s:
            g2.append(n*k)
            done.add(n*k)
    return len(max([g1, g2], key=len))


ans = main()
print(ans)

# try:
#     ans = main()
#     print(ans)
# except Exception as e:
#     # print(e)
#     traceback.print_exc()