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.HashSet;
import java.util.Scanner;


public class CF274A {

    public static void main(String[] args) throws Exception {
        new CF274A().solve();
    }

    private void solve() throws Exception {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        long k = sc.nextInt();
        Integer[] a = new Integer[n];
        for (int i = 0; i < n; i++) {
            a[i] = sc.nextInt();
        }
        Arrays.sort(a);
        HashSet<Integer> used = new HashSet<>(n);
        int count = 0;
        for (int i = 0; i < n; i++) {
            Integer v = a[i];
            if (!used.contains(v)) {
                count++;
                long next = v * k;
                if (next <= 1000000000) used.add((int) next);
            }
        }
        System.out.println(count);
    }

}
