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.PrintWriter;
import java.util.Scanner;


public class nB {

    Scanner in;
    PrintWriter out;
    
    void solve(){
        int n = in.nextInt();
        int m = in.nextInt();
        int k = in.nextInt();
        int a[] = new int[m];
        for (int i = 0; i < m; i++){
            a[i] = in.nextInt();
        }
        int fed = in.nextInt();
        int ans = 0;
        for (int i = 0; i < m; i++){
            int check = fed ^ a[i];
            int count = 0;
            String s = Integer.toBinaryString(check);
            for (int j = 0; j < s.length(); j++){
                if (s.charAt(j) == '1'){
                    count++;
                }
            }
            if (count <= k){
                ans++;
            }
        }
        out.println(ans);
       /* String s[] = new String[m];
        for (int i = 0; i < m; i++){
            a[i] = in.nextInt();
            s[i] = Integer.toBinaryString(a[i]);
            StringBuilder sb = new StringBuilder(s[i]);
            sb.reverse();
            s[i] = sb.toString();
        }
        int fed = in.nextInt();
        String temp = Integer.toBinaryString(fed);
        int ans = 0;
        for (int i = 0; i < m; i++){
            int count = 0;
            for (int j = 0; j < Math.max(temp.length(), s[i].length()); j++){
                char tb = '0';
                char stb = '0';
                if (j < temp.length()){
                    tb = temp.charAt(j);
                }
                if (j < s[i].length()){
                    stb = s[i].charAt(j);
                }
                if (tb != stb){
                    count++;
                }
            }
            if (count <= k){
                ans++;
            }
        }
        out.println(ans);*/
    }
    
    void run(){
        in = new Scanner(System.in);
        out = new PrintWriter(System.out);
        try{
            solve();
        }finally{
            out.close();
        }
    }
    public static void main(String[] args) {
        new nB().run();
    }

}