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:


/**
 * Created by Hp on 3/28/2016.
 */
import java.util.*;
public class FedoorAndGame {
    public static void main(String [] ar){
        Scanner s=new Scanner(System.in);
        int n=s.nextInt();
        int m=s.nextInt();
        int k=s.nextInt();
        int []x=new int[m+1];

        for(int i=0;i<=m;i++){
            x[i]=s.nextInt();
        }
        int count=0;
        for(int i=0;i<m;i++){
            //System.out.println(Integer.toBinaryString(x[m]));
            //System.out.println(Integer.toBinaryString(x[i])+" "+Integer.toBinaryString(x[m]^x[i]));
            if(Integer.bitCount(x[m]^x[i])<=k)
                count++;
        }
        System.out.println(count);
    }
}