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:
/* BY - LAXMIKANT KATRE */

import java.io.*;
import java.util.*;
 
public class Main {
    
    static MyScanner sc = new MyScanner();
    
    public static void main(String[] args) {
        
        int n = sc.nextInt();
        int m = sc.nextInt();
        int k = sc.nextInt();
        
        int[] arr = init(m);
        int fedo = sc.nextInt();
        int count = 0;
        for(int i = 0; i < m; ++i) {
            
            if(Integer.bitCount(arr[i] ^ fedo) <= k)
                ++count;
        }
        
        out.println(count);
        
        out.close();
 
    }
    
    
/*****************************************************************************/
    
    // array of int type taking input
    public static int[] init(int n) {
        
        int[] arr = new int[n];
        
        for(int i = 0; i < n; ++i)
            arr[i] = sc.nextInt();
            
        return arr;
    }
    
    //return gcd of two numbers
    public static int gcd(int a, int b) {
        
        if(a == 0)
            return b;
            
        return gcd(b % a, b);
    }
    
    
    //checks whether a number is prime or not
    public static boolean prime(int n) {
        
        if(n < 2)
            return false;
        
        for(int i = 2; i * i <= n; ++i)
            if(n % i == 0)
                return false;
                
        return true;
    }
    
/***************************************************************************/
    
                        /****        Fast I/O        ****/
    
    
    //-----------PrintWriter for faster output---------------------------------
    public static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));;

    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;
 
        public MyScanner() {
            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;
        }
    }
    //--------------------------------------------------------
}