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 math
from  collections import defaultdict

# sys.stdin = open('input.txt', 'r')
# sys.stdout = open('output.txt', 'w')

def solve(test):
	n, k = map(int, input().split())
	a = list(map(int, input().split()))
	a.sort(reverse = True)
	rec = set()
	for i in range(n):
		if a[i] * k not in rec:
			rec.add(a[i])

	ans = len(rec)
	print(ans)





if __name__ == "__main__":
	test_cases = 1
	for t in range(1, test_cases + 1):
		solve(t)

	  					 			  			 			   		 	  	