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, threading

sys.setrecursionlimit(10 ** 6)

scan = lambda: map(int, input().split())

n, k = scan()
arr = list(scan())
dic = {}
arr.sort()
for i in arr:
    if i%k == 0:
        if dic.get(i/k, 0):
            continue
    if dic.get(i, 0):
        dic[i] += 1
    else:
        dic[i] = 1
ans = 0
for i in dic:
    ans += dic[i]
print(ans)