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.*;
import java.util.*;

public class CodeF
{
    public static void main(String[] args)throws IOException
    {
      BufferedReader br=new BufferedReader(new InputStreamReader(System.in));

		String []s=br.readLine().split(" ");
        int n=Integer.parseInt(s[0]);
        int m=Integer.parseInt(s[1]);
        int k=Integer.parseInt(s[2]);
        
        int a[]=new int[m+1];
        
        for(int i =0; i<m+1; i++)
        	a[i]=Integer.parseInt(br.readLine());
        
        int count=0;
        
        //sort array in ascending order
		  //Arrays.sort(a);
		  
		for(int i =0; i<m; i++)
		{
		 	if (Integer.bitCount(a[i]^a[m]) <=k)
		  		count++;
        }
                
        
        System.out.println(count);
        
    }
}