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.Arrays;
import java.util.Scanner;

public class C {
	public static void main(String[] args) {	
		Scanner theIn=new Scanner(System.in);
		int n=theIn.nextInt();
		long k=theIn.nextLong();
		
		Long[] t=new Long[n];
		for (int i=0; i<n; i++) {
			t[i]=theIn.nextLong();
		}
		if (k==1) {
			System.out.println(n);
			return;
		}
		Arrays.sort(t);
		int j=0;
		int s=0;
		for (int i=0; i<n; i++) {
			if (t[i]==0) continue;
			long w=t[i]*k;
			if (w<0) break;
			while (j<n && t[j]<w) j++;
			if (j>=n) break;
			if (t[j]==w) {
				s++;
				t[j]=(long) 0;
			}
		}
		System.out.println(n-s);
		
	}
}