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.*;
import java.util.*;

public class Main {

    private  static void solver(InputReader sc, PrintWriter out) throws Exception {
        int n  = sc.nextInt();
        int m = sc.nextInt();
        int k = sc.nextInt();
        int arr[] = sc.readIntArr(m+1);
        int boi = arr[m];
        int fincount=0;
        for(int i=0; i<m; i++){
            int count=0;
            String s = Long.toBinaryString((boi ^ arr[i]));
            for(int j=0,len=s.length(); j<len; j++){
                if(s.charAt(j)=='1')
                    count++;
            }
            if(count<=k) {
                fincount++;
              //  System.out.println(arr[i]+" "+s);
            }
           // System.out.println(arr[i]+" "+s);
        }
        out.println(fincount);
    }

    public static void main(String[] args) throws Exception{
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);

        solver(in,out);
        out.close();
    }
    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong(){
            return Long.parseLong(next());
        }

        public long[] readLongArr(int n){
            long arr[] = new long[n];
            for(int i=0; i<n; i++){
                arr[i] = nextLong();
            }
            return arr;
        }
        public int[] readIntArr(int n){
            int arr[] = new int[n];
            for(int i=0; i<n; i++){
                arr[i] = nextInt();
            }
            return arr;
        }
    }
}
class Pair{
    long x;
    boolean bool;
    Pair(long x, boolean bool){
        this.x = x;
        this.bool = bool;
    }
}