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:
/**
 *
 * @author Faruk
 */

import java.util.Arrays;
import java.util.Scanner;
import java.util.HashSet;
import java.util.HashMap;
import java.util.ArrayList;


public class tmp {
    public static void main(String [] args){
        Scanner scan = new Scanner(System.in);

        int n = scan.nextInt();
        int m = scan.nextInt();
        int k = scan.nextInt();
        int friend = 0;
        int [] arr = new int[m+1];
        
        for(int i=0; i<=m; i++){
            arr[i] = scan.nextInt();
        }
        int tmp= 0;
        int tmp1;
        for(int i=0; i<m; i++){
            tmp1 = k;
            tmp = arr[i]^arr[m];
            while(tmp1>0){
                tmp1--;
                tmp &= (tmp-1);
                if(tmp == 0){
                    friend++;
                    break;    
                }
            }
        }
        System.out.println(friend);
        
        
        
        
        
        
        
    }

}