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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.util.ArrayList;

public class FedorandNewGame {

    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        OutputStream out = new BufferedOutputStream(System.out);
        String[] l = br.readLine().split("\\s+");
        int n = Integer.parseInt(l[0]);
        int m = Integer.parseInt(l[1]);
        int k = Integer.parseInt(l[2]);
        ArrayList<String> list = new ArrayList<String>(m + 1);

        for (int i = 0; i <= m; i++) {
            int army = Integer.parseInt(br.readLine());
            String s = Integer.toBinaryString(army);

            while (s.length() < n)
                s = "0" + s;
            list.add(s);
        }

        String f = list.get(m);
        int res = 0;
        for (int i = 0; i < m; i++) {
            int count = 0;

            for (int j = 0; j < n; j++)
                if (list.get(i).charAt(j) != f.charAt(j))
                    count++;

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

        out.write((res + "").getBytes());

        out.flush();
        br.close();

    }

}