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
input = lambda: sys.stdin.readline().rstrip()

N,K = map(int, input().split())
A = list(map(int, input().split()))

B = {}
for i,a in enumerate(A):
    B[str(a)] = i

P = [[] for _ in range(N)]
for i,a in enumerate(A):
    key = str(a*K)
    #print(i,a,key, key in B)
    if key in B:
        j = B[key]
        P[i].append(j)
        P[j].append(i)
    
seen = [-1]*N

def paint(idx, color):
    v = [idx]
    while v:
        i = v.pop()
        if seen[i]!=-1:continue
        seen[i] = color
        
        for j in P[i]:
            if seen[j]!=-1:continue
            v.append(j)

color = 0
for i in range(N):
    if seen[i]==-1:
        color+=1
        paint(i,color)

# print(P)
# print(seen)
print(color)

