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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Set;
import java.util.TreeMap;

public class FreeSet {

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] values = br.readLine().split(" ");
		int n = Integer.parseInt(values[0]);
		long k = Integer.parseInt(values[1]);
		String[] ai_strings = br.readLine().split(" ");
		if (k==1){
			System.out.println(n);
			return;
		}
		
		TreeMap<Integer, Integer> hm = new TreeMap<Integer, Integer>();
		for(int i=0; i<n; i++){
			int ai = Integer.parseInt(ai_strings[i]);
			hm.put(ai, 1);
		}
	    Set<Integer> keys = hm.keySet();
	    for(int key: keys){
	        if(hm.get(key) == 1){
	        	long next = key*k;
	        	if(next > Math.pow(10, 9)) continue;
	        	if(hm.get((int)next) != null)
	        		hm.put((int)(next), 0);
	        }
	    }
	    int ans = 0;
	    for(int key: keys){
	    	ans += hm.get(key);
	    }
	    System.out.println(ans);
	}

}
