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 < 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.

Input

The first line of the input contains two integers n and k (1 ≤ n ≤ 105, 1 ≤ k ≤ 109). The next line contains a list of n distinct positive integers a1, a2, ..., an (1 ≤ ai ≤ 109).

All the numbers in the lines are separated by single spaces.

Output

On the only line of the output print the size of the largest k-multiple free subset of {a1, a2, ..., an}.

Examples

Input

6 2
2 3 6 5 4 10


Output

3

Note

In the sample input one of the possible maximum 2-multiple free subsets is {4, 5, 6}.
n, k = map(int, raw_input().split())
A = map(int, raw_input().split())

C = {}
for e in A:
    C[e] = C.get(e, 0) + 1
B = sorted(set(A))

if k==1:
    print len(B)
    exit(0)

s = set(A)
used = set()
ans = 0
for e in B:
    if e in used: continue
    cnts = [0]*2
    i = 0
    used.add(e)
    cnts[0] = C[e]
    while e*k in s:
        e *= k
        i += 1
        cnts[i%2] += C[e]
        used.add(e)
    ans += max(cnts)
print ans
