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;

/**
 * 
 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.
 * 
 * 
 * Sample test(s)
 * 
 * 
 * 
 * Input 7 3 1 8 5 111 17
 * 
 * 
 * 
 * Output 0
 * 
 * 
 * 
 * Input 3 3 3 1 2 3 4
 * 
 * 
 * 
 * Output 3
 * 
 * B467FedorAndNewGame.java
 * 
 * @author olivelv
 * @version time: Sep 22, 2015 11:09:33 PM
 */
public class Main{
    public static void main(String []args){
        Scanner cin=new Scanner(System.in);
        int n=cin.nextInt();
        int m=cin.nextInt();
        int k=cin.nextInt();
        int []p=new int[m];
        for(int i=0;i<m;i++)p[i]=cin.nextInt();
        int f=cin.nextInt();
        int num=0;
        for(int i=0;i<m;i++){
            int val=p[i]^f;
            int s=0;
            while(val!=0){
                s+=val&1;
                val>>=1;
            }
            if(s<=k)num++;
        }
        System.out.println(num);
    }
}