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.FileInputStream;
import java.io.FileNotFoundException;
import java.util.*;

public class Main {

    private static Scanner scanner;

    static void solution() {
        int n = scanner.nextInt();
        int m = scanner.nextInt();
        int k = scanner.nextInt();

        String[] players = new String[m];
        for (int i = 0; i < m; i++) {
            players[i] = String.format("%20s", Integer.toBinaryString(scanner.nextInt())).replace(' ', '0');
        }

        String fedor = String.format("%20s", Integer.toBinaryString(scanner.nextInt())).replace(' ', '0');

        int friends = 0;
        for (int i = 0; i < m; i++) {
            int count = 0;
            for (int j = 19; j > 19-n; j--) {
                if (players[i].charAt(j) != fedor.charAt(j)) {
                    count++;
                }
            }

            if (count <= k) friends++;
        }

        System.out.println(friends);
    }


    public static void main(String args[]) {
        scanner = new Scanner(System.in);
        solution();
    }
}