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 java.util.*;
public class P274A {
	P274A(Scanner in) {
		int N = in.nextInt();
		long K = in.nextInt();
		TreeSet<Long> inSet = new TreeSet<Long>();
		long[] vals = new long[N];
		for (int i=0; i<N; i++) {
			vals[i] = in.nextInt();
			inSet.add(vals[i]);
		}
		Arrays.sort(vals);
		int ans = 0;
		for (long i: vals)
			if (inSet.contains(i)) {
				long x = i;
				int size = 0;
				while(inSet.contains(x)) {
					size++;
					inSet.remove(x);
					x=x*K;
				}
				ans += (size+1)/2;
			}
		System.out.println(ans);
	}
	public static void main(String[] args) {
		new P274A(new Scanner(System.in));
	}
}
