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}.
import sys
import collections
import bisect

n, k = map(int, sys.stdin.readline().split())
seq = map(int, sys.stdin.readline().split())

seq.sort(reverse=True)
cand = set(seq)
if k == 1:
    print len(cand)
    sys.exit(0)
for s in seq:
    if s / k <= 0:
        break
    if s not in cand:
        continue
    if s % k == 0 and s / k in cand:
        cand.remove(s / k)
print len(cand)