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.*;
import java.lang.Math; 
import java.util.Arrays;
import java.util.Scanner;
import java.util.stream.IntStream;
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;

/*
    ██╗███╗   ███╗███████╗██╗  ██╗██╗██╗   ██╗ █████╗ ███╗   ███╗
    ██║████╗ ████║██╔════╝██║  ██║██║██║   ██║██╔══██╗████╗ ████║
    ██║██╔████╔██║███████╗███████║██║██║   ██║███████║██╔████╔██║
    ██║██║╚██╔╝██║╚════██║██╔══██║██║╚██╗ ██╔╝██╔══██║██║╚██╔╝██║
    ██║██║ ╚═╝ ██║███████║██║  ██║██║ ╚████╔╝ ██║  ██║██║ ╚═╝ ██║
    ╚═╝╚═╝     ╚═╝╚══════╝╚═╝  ╚═╝╚═╝  ╚═══╝  ╚═╝  ╚═╝╚═╝     ╚═╝
*/
public class Problem {
   	public static void main(String[] args) {
	   InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskA solver = new TaskA();
        solver.solve(1, in, out);
        out.close();
	}
	
	static class TaskA {
          public void solve(int testNumber, Scanner in, PrintWriter out) {
              int n = in.nextInt();
              int m = in.nextInt();
              int k = in.nextInt();
              int[] x = new int[m+1];
              
              for(int i=0;i<m+1;i++)
                 x[i] = in.nextInt();
             
             int f =0;
              for(int i=0;i<m;i++){
                   			if(Integer.bitCount(x[i] ^ x[m]) <=k) f++;
              }  
              out.print(f);
	     }  
	} 
}