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.util.*;

/**
 * Created by Firеfly on 23.08.2016.
 */
public class First {
    public static void main(String[] args) throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        // String[] mas = reader.readLine().split(" ");
       // int a = Integer.parseInt(mas[0]);
        String[] mas = reader.readLine().split(" ");
        int n = Integer.parseInt(mas[0]);
        int k = Integer.parseInt(mas[1]);
        int z = Integer.parseInt(mas[2]);
        int[] enem = new int[k];
        for (int i = 0; i<k; i++)
            enem[i] = Integer.parseInt(reader.readLine());
        int pers = Integer.parseInt(reader.readLine());
        int count = 0;
        for (int j = 0; j<enem.length; j++) {
            int copy = pers;
            int pcount = 0;
            for (int i = n-1; i>=0; i--) {
                if ((copy >>> i) != (enem[j]>>>i)) {
                    enem[j] = enem[j] ^ upper(2, i);
                    pcount++;
                }
            }
            if (pcount<=z)
                count++;
        }
        System.out.println(count);

        }
    static int upper(int i, int n) {
        if (n==0) return 1;
        ArrayList<Integer> list = new ArrayList<>();
        while (n!=1)
        {
            if (n%2 == 0) {
                i *= i;
                n /= 2;
            }
            else {
                list.add(i);
                i *= i;
                n -= 1;
                n /= 2;
            }

        }
        for (int k = 0; k<list.size(); k++)
            i*=list.get(k);
        return i;
    }
}