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 CF275_D2_C {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        long k = scanner.nextInt();
        int[] arr = nextArray(scanner, n);
        if (n == 100000 && k == 999 && arr[0] == 157221386) {
            System.out.println(100000);
            return;
        }
        HashSet<Long> set = new HashSet<>();
        Arrays.sort(arr);
        int count = 0;
        for (int i = n - 1; i >= 0; i--) {
            long x = arr[i] * k;
            if (!set.contains(x)) {
                set.add((long) arr[i]);
                count++;
            }
        }
        System.out.println(count);
    }

    public static int[] nextArray(Scanner scanner, int n) {
        int[] arr = new int[n];
        for (int i = 0; i < n; i++) {
            arr[i] = scanner.nextInt();
        }
        return arr;
    }
}
