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:
/*
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 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */

import java.util.*;

/**
 *
 * @author Abhijit
 */
public class Fidor {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        // TODO code application logic here
        Scanner sc=new Scanner(System.in);
        int  n=sc.nextInt(),m=sc.nextInt(),k=sc.nextInt(),num,count=0,total=0;
        String str[]=new String[m+2];
        for(int i=1;i<m+2;i++){
            num=sc.nextInt();
            str[i]=Integer.toBinaryString(num);
        }
        for(int i=1;i<m+1;i++){
            count=0;
            //System.out.println(str[i]+" "+str[m+1]);
            if(str[i].length()<str[m+1].length()){
                int z1=str[m+1].length()-1,z2=str[i].length()-1;
                while(z2>=0){
                    if(str[i].charAt(z2)!=str[m+1].charAt(z1))
                        count++;
                    z1--;
                    z2--;
                }
                while(z1>=0){
                    if(str[m+1].charAt(z1)!='0')
                        count++;
                    z1--;
                }
                if(count<=k)
                	total++;
            }
            else if(str[i].length()>=str[m+1].length()){
                int z1=str[m+1].length()-1,z2=str[i].length()-1;
                while(z1>=0){
                    if(str[i].charAt(z2)!=str[m+1].charAt(z1))
                        count++;
                    z1--;
                    z2--;
                }
                while(z2>=0){
                    if(str[i].charAt(z2)!='0')
                        count++;
                    z2--;
                }
                if(count<=k)
                	total++;
            }
        }
        System.out.println(total);
    }
}