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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

/**
 * Created by dtnha on 10/18/2017.
 */
public class FedorAndNewGame {

    private static class Reader {
        static BufferedReader reader;
        static StringTokenizer tokenizer;

        /**
         * call this method to initialize reader for InputStream
         */
        public static void init(InputStream input) {
            reader = new BufferedReader(
                    new InputStreamReader(input));
            tokenizer = new StringTokenizer("");
        }

        /**
         * get next word
         */
        public static String next() throws IOException {
            while (!tokenizer.hasMoreTokens()) {
                //TODO add check for eof if necessary
                tokenizer = new StringTokenizer(
                        reader.readLine());
            }
            return tokenizer.nextToken();
        }

        public static int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public static long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public static double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }
    }

    public static void main(String[] args) throws IOException {
        Reader.init(System.in);

        int n = Reader.nextInt();
        int m = Reader.nextInt();
        int k = Reader.nextInt();

        int[] x = new int[m + 1];
        for (int i = 1; i <= m; i++) {
            x[i] = Reader.nextInt();
        }
        int fedorX = Reader.nextInt();
        int count = 0;
        for (int i = 1; i <= m; i++) {
            if (isFriends(fedorX, x[i], k)) {
                count++;
            }
        }

        System.out.println(count);
    }

    private static boolean isFriends(int fedorX, int i, int k) {

        int y = fedorX ^ i;

        int count = 0;
        while (y > 0) {
            if(y%2==0){
                y = y/2;
            }else{
                count++;
                y--;
            }
        }

        return (count <= k);

    }


}