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 k_Multiple_Free_Set {

    public static void main(String[] args) {
        int n,k,j=0,index;
        Scanner s=new Scanner (System.in);
        n=s.nextInt();
        k=s.nextInt();
        int [] a = new int[n];
        int [] b = new int[n];
        for (int i=0;i<n;i++) a[i] = s.nextInt();
        Arrays.sort(a);
         b[0] = a[0]; 
        for (int i=1;i<n;i++){
            if (a[i]%k==0) {
                index=Arrays.binarySearch(b, 0, j+1,a[i]/k);
                if (index < 0 || index>j) b[++j] = a[i]; 
            }
            else b[++j] = a[i];
        }
        System.out.println(j+1);
    }
}