Problem: After you had helped George and Alex to move in the dorm, they went to help their friend Fedor play a new computer game «Call of Soldiers 3».

The game has (m + 1) players and n types of soldiers in total. Players «Call of Soldiers 3» are numbered form 1 to (m + 1). Types of soldiers are numbered from 0 to n - 1. Each player has an army. Army of the i-th player can be described by non-negative integer xi. Consider binary representation of xi: if the j-th bit of number xi equal to one, then the army of the i-th player has soldiers of the j-th type. 

Fedor is the (m + 1)-th player of the game. He assume that two players can become friends if their armies differ in at most k types of soldiers (in other words, binary representations of the corresponding numbers differ in at most k bits). Help Fedor and count how many players can become his friends.

Input

The first line contains three integers n, m, k (1 ≤ k ≤ n ≤ 20; 1 ≤ m ≤ 1000).

The i-th of the next (m + 1) lines contains a single integer xi (1 ≤ xi ≤ 2n - 1), that describes the i-th player's army. We remind you that Fedor is the (m + 1)-th player.

Output

Print a single integer — the number of Fedor's potential friends.

Examples

Input

7 3 1
8
5
111
17


Output

0


Input

3 3 3
1
2
3
4


Output

3

Solution (in JAVA):

Solution:
import java.util.*;
public class CF467B 
{

	/**
	 * @param args
	 */
	static int [] toBits(int n,int k)
	{
		int ans[]=new int[k];
		for (int i = 0; i < ans.length; i++) 
		{
			ans[i]=n%2;
			n=n/2;
		}
		return ans;
	}
	public static void main(String[] args) 
	{
		Scanner sc=new Scanner(System.in);
		int n,m,k,f,ans=0,diff=0;;
		n=sc.nextInt();
		m=sc.nextInt();
		k=sc.nextInt();
		int pl[]=new int[m];
		for (int i = 0; i < pl.length; i++) 
		{
			pl[i]=sc.nextInt();
		}
		 f=sc.nextInt();
		 int comp[]=new int[n];
		 comp=toBits(f,n);
		 for (int i = 0; i < pl.length; i++) 
		 {
			 diff=0;
			 int c[]=toBits(pl[i],n);
			 for(int j=0;j<n;j++)
			 {
				 if(comp[j]!=c[j])
					 diff++;
			 }
			if(diff<=k)
				ans++;
		 }
		 System.out.println(ans);
		// TODO Auto-generated method stub

	}

}