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.util.*;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
 
public class Main {
   static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;
 
        public FastReader()
        {
            br = new BufferedReader(new
                     InputStreamReader(System.in));
        }
 
        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        int nextInt()
        {
            return Integer.parseInt(next());
        }
 
        long nextLong()
        {
            return Long.parseLong(next());
        }
 
        double nextDouble()
        {
            return Double.parseDouble(next());
        }
 
        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }
    static String getBinary (int n) {
        StringBuilder sb = new StringBuilder(100);
        while (n > 0) {
            sb.insert(0, n % 2);
            n = n/2;
        }
        return sb.toString();
    }
    
    static int getNumberofOnes(int n) {
        String s = getBinary(n);
        /*System.out.println(n);
        System.out.println(s);*/
        int count = 0;
        for (int i=0; i<s.length(); i++) {
            if(s.charAt(i) == '1') {
                count++;
            }
        }
        //System.out.println(count);
        return count;
    }
        public static void main(String args[]) {
        FastReader s = new FastReader();
        
        int N = s.nextInt();
        int M = s.nextInt();
        int K = s.nextInt();
        int arr[] = new int[M+1];
        for (int i=0; i<M+1; i++) {
            arr[i] = s.nextInt();
        }
        //System.out.println(arr[M]);
        int friends = 0;
        for (int j=0; j<M; j++) {
            if (getNumberofOnes(arr[M] ^ arr[j]) <= K) {
                friends++;
            }
        }
        System.out.println(friends);
    }
}