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.io.*;
public class Main {
    static int countSetBits(int n)
    {
        int count = 0;
        while (n!=0)
        {
            n &= (n-1) ;
            count++;
        }
        return count;
    }
    public static void main(String args[])throws IOException
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        String in[]=(br.readLine()).split(" ");
        int n=Integer.parseInt(in[0]);
        int m=Integer.parseInt(in[1]);
        int k=Integer.parseInt(in[2]);
        int x[]=new int[m];
        int f=0;
        int i=0;
        while(i<m)
        {
            x[i]=Integer.parseInt(br.readLine());
            i++;
        }
        f=Integer.parseInt(br.readLine());
        
        int count=0;
        for(i=0;i<m;i++)
        {
         int temp=f^x[i];
         if(countSetBits(temp)<=k)
             count++;
        }
        System.out.println(count);
    }
}