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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class ProplemSolving {

    public static void main(String[] args) throws IOException {
        
        BufferedReader r=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer in=new StringTokenizer(r.readLine());
        
        int n=Integer.parseInt(in.nextToken());
        int m=Integer.parseInt(in.nextToken());
        int k=Integer.parseInt(in.nextToken());
        
        String a[]=new String[m];
        for(int i=0;i<m;i++){
            a[i]=bin(Integer.parseInt(r.readLine()));
        }
        String f=bin(Integer.parseInt(r.readLine()));
        
        //_____________________________________________\\
        int coun=0;
        int com=0;
        
        for(int i=0;i<m;i++){
            for(int j=0;j<20;j++){
                if(a[i].charAt(j)!=f.charAt(j))com++;
            }
            if(com<=k)coun++;
            com=0;
        }
        System.out.println(coun);
        
    }
    public static String bin(int n){
        int []ans=new int[20];
        String ans2="";
        int index=19;
        while(n!=0){
            ans[index]=n%2;
            n/=2;
            index--;
        }
        for(int i=0;i<ans.length;i++){
            ans2+=ans[i]+"";
        }
        return ans2;
    }
    
}