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.awt.Point;
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.File;
import java.io.FileReader;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Hashtable;

public class Main {

    static String fileName = "input.txt";
    
    public static void main(String[] args) throws Exception {
        
//      BufferedReader in = new BufferedReader(new FileReader(new File(fileName)));
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        
        int n,m,k;
        String s;
        s = in.readLine();
        String l[] = s.split(" ");
        n = Integer.parseInt(l[0]);
        m = Integer.parseInt(l[1]);
        k = Integer.parseInt(l[2]);
        
        m++;
        ArrayList<Integer> list = new ArrayList<Integer>();
        for(int i = 0; i < m;i++) {
            list.add(Integer.parseInt(in.readLine()));
        }
        
        int x= list.get(m-1);
        int counter = 0;
        int z;
        int ff;
        for(int i = 0; i < m-1; i++) {
            z = x ^ list.get(i);
            s = new BigInteger(""+z).toString(2);
            ff = 0;
            for(int j = 0;j < s.length() && ff <= k; j++) {
                if(s.charAt(j) == '1')
                    ff++;
            }
            
            if(ff <= k)
                counter++;
        }
        
        System.out.println(counter);
        in.close();
        
    }
    
    
    
    
}