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.InputStreamReader;
import java.io.PrintWriter;

public class B467 {
    public static void main(String[] args) {

        try (BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
             PrintWriter writer = new PrintWriter(System.out)) {
            new B467().run(reader, writer);
        } catch (IOException e) {
            e.printStackTrace();
        }
    }

    public static long[] parseLongs(String s) {
        String[] toParse = s.split(" ");
        long[] toReturn = new long[toParse.length];
        for (int i = 0; i < toParse.length; i++) {
            toReturn[i] = Long.parseLong(toParse[i]);
        }
        return toReturn;
    }

    public void run(BufferedReader in, PrintWriter out) throws IOException {
        long[] input = parseLongs(in.readLine());
        int n = (int)input[0];
        int m = (int)input[1];
        int k = (int)input[2];
        int[] soldiers = new int[m];

        for (int i = 0; i < m; i++) {
            soldiers[i] = Integer.parseInt(in.readLine());
        }

        int soldier = Integer.parseInt(in.readLine());

        int answer = 0;

        for (int mask : soldiers) {
            int count = 0;
            for (int pos = 0; pos < n; pos++) {
                if (((1 << pos) & mask) != ((1 << pos) & soldier)){
                    count++;
                }
            }
            if (count <= k) {
                answer++;
            }
        }

        out.println(answer);
    }
}