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.Scanner;
import java.util.ArrayList;
public class MyClass {
    
     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[] friends = new int[m];
     for(int i = 0; i<m; i++)
     {
         friends[i] = scan.nextInt(); 
     }
     int fedor = scan.nextInt();
     int count = 0;
     for(int j = 0; j<m; j++)
     {
         int diff = friends[j]^fedor;
         String s = Integer.toString(diff,2);
         int diffCount = 0;
         for(int i = 0; i<s.length(); i++)
         {
             if(s.charAt(i) == '1')
                diffCount++; 
         }
         if(diffCount <= k)
             count++;
     }
    
     System.out.println(count);     
          
     
  }  
}