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.BitSet;
import java.util.Scanner;

public class Main {
    Scanner sc = new Scanner(System.in);

    void run() {
        int n = sc.nextInt();
        int k = sc.nextInt();

        int list[] = new int[n];
        for (int i = 0; i < n; i++) {
            list[i] = sc.nextInt();
        }
        Arrays.sort(list);
        if (k == 1) {
            System.out.println(n);
            return;
        }
        BitSet map = new BitSet(500000000);
        int res = n;
        for (int i = 0; i < n; i++) {
            if (list[i] % k == 0) {
                if (map.get(list[i] / k)) {
                    res--;
                    continue;
                }
            }
            map.set(list[i]); 
        }
        System.out.println(res);
    }

    public static void main(String[] a) {
        Main m = new Main();
        m.run();
    }
}
