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;

public class Problem467B {
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt(); //types of soldiers in total 
    int m = sc.nextInt(); //number of player except Fedor 
    int k = sc.nextInt(); //at most bit
    int[] players = new int[m+1];
    int count =0;
    long result =0;
    for(int i=0; i<(m+1); i++) {
      players[i] = sc.nextInt();
    }
    
    for(int i=0; i<m; i++) {
      result = players[i] ^ players[m];
      if(countBits(result)<=k) {
        count++;
      }   
    }
    System.out.println(count);
    sc.close();
   }
   private static int countBits(long n) {
     int c =0;
     while(n !=0) {
       n = n & n-1;
       c++;
     }
     return c;
   }
 }