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 binsearch(X, start, end, search):
    while (start < end):
        mid = (start + end) // 2
        if X[mid] == search:
             return mid
        elif X[mid] > search:
            end = mid
        else:
            start = mid + 1
    return -1


def main():
    n, k = list(map(int, input().split()))
    X = list(map(int, input().split()))
    X.sort()
    count = 0
    for i in range(n):
        if binsearch(X, 0, len(X), X[i] * k) == -1:
            count += 1
    print(count)


if __name__ == "__main__":
    main()