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.BufferedInputStream;
import java.io.BufferedOutputStream;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * User: anatoly
 * Date: 25.06.13
 * Time: 0:04
 */
public class P467B {
    private static final BufferedInputStream is = new BufferedInputStream(System.in);
    private static final Scanner s = new Scanner(is);
    private static final BufferedOutputStream os = new BufferedOutputStream(System.out);
    private static final PrintWriter out = new PrintWriter(os);


    public static void main(String[] args) {
        try {
            solve();
            out.flush();
            os.flush();
        } catch (IOException e) {
        }
    }


    public static void solve() throws IOException {
        int n = s.nextInt();
        int m = s.nextInt();
        int k = s.nextInt();
        int[] xs = new int[m + 1];

        for (int i = 0; i < m + 1; i++) {
            xs[i] = s.nextInt();
        }

        int myArmy = xs[m];
        int res = 0;
        for (int i = 0; i < m ; i++) {
            int diff = xs[i] ^ myArmy;
            int diffCount = 0;
            for (int j = 0; j < n; j++) {
                if ((diff & 0x1)==0x1) {
                    diffCount++;
                }
                diff >>>= 1;

            }
            if (diffCount <= k) {
                res++;
            }
        }

        System.out.println(res);

    }


}