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 math

MAXNUM = math.inf
MINNUM = -1 * math.inf


def getInts():
    return map(int, sys.stdin.readline().rstrip().split(" "))


def getString():
    return sys.stdin.readline().rstrip()


def solve(n, k, ints):
    cache = {}
    total = 0

    for ele in ints:
        length = 1
        if (ele * k) in cache:
            after = ele * k
            end = cache[after][1]  # 1 is end of series
            total -= ((cache[after][2]) + 1) // 2  # max length of this sequence
            length += cache[after][2]
        else:
            end = ele

        if ele % k == 0 and (ele // k) in cache:
            before = ele // k
            start = cache[before][0]  # 0 is start of series
            total -= ((cache[before][2]) + 1) // 2  # length
            length += cache[before][2]
        else:
            start = ele

        cache[start] = (start, end, length)
        cache[end] = (start, end, length)
        total += ((length) + 1) // 2

    return total


def printOutput(ans):
    sys.stdout.write(str(ans))


def readinput():
    n, k = getInts()
    ints = list(getInts())
    printOutput(solve(n, k, ints))


readinput()
