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 Main 
{
    public void work()
    {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int m = sc.nextInt();
        int k = sc.nextInt();
        
        int people[] = new int[m+1];
        for(int i=0; i<=m; i++)
            people[i] = sc.nextInt();
        
        int fedor = people[m];
        int count = 0;
        
        for(int i=0; i<m; i++)
        {
            //if guy and fedors corresponding bits are different, increment count
            //if count > k, terminate
            //at end, increment
            
            int num = people[i] ^ fedor;
            boolean eligible = true;
            
            int ones = 0;
            while(num > 0)
            {
                ones++;
                if(ones > k)
                {
                    eligible = false;
                    break;
                }
                num = num & num-1;
            }
            
            if(eligible)
                count++;
        }
        System.out.println(count);
    }
    
    public static void main(String[] args) 
    {
        Main ob = new Main();
        ob.work();
    }

}