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.*;
import java.math.BigInteger;

public class A 
{
    FastScanner in;
    PrintWriter out;
    
    public boolean check (int x, int fed, int n, int k)
    {
            
        while (n-- > 0)
        {
            if ((x % 2) != (fed % 2)) k--;
                    
            if (k < 0)
                return false;
            
            x /= 2;
            fed /= 2;
        }
        return true;
    }
    
    public void solve() throws IOException
    {
        int n = in.nextInt();
        int m = in.nextInt();
        int k = in.nextInt();
        
        int mas[] = in.nextIntArray(m);
        int fedor = in.nextInt();
        
        int count = 0;
        
        for (int i = 0; i < m; i++)
            if ( check(mas[i], fedor, n, k) == true) count++;
            
        out.println(count);
    }
                
            

    public void run() 
    {
        try 
        {
            //in  = new FastScanner(new File("sum.in"));
            //out = new PrintWriter(new File("sum.out"));
            
            in  = new FastScanner();
            out = new PrintWriter(System.out);

            solve();

            out.close();
        }
        catch (IOException e) 
        {
            e.printStackTrace();
        }
    }

    class FastScanner 
    {
        BufferedReader  br;
        StringTokenizer st;
        
        FastScanner() 
        {
            br = new BufferedReader(new InputStreamReader(System.in));        
        }

        FastScanner(File f) 
        {
            try
            {
                br = new BufferedReader(new FileReader(f));
            }
            catch (FileNotFoundException e) 
            {
                e.printStackTrace();
            }
        }

        String nextLine() 
        {
            String ret = null;
            try
        {
                ret = br.readLine();
        }
        catch (IOException e)
        {
            e.printStackTrace();
        }
            
            return ret;
        }

        String next() 
        {
            while (st == null || !st.hasMoreTokens()) 
            {
                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());
        }
        
        int[] nextIntArray(int size) 
        {
            int[] array = new int[size];
            
            for (int i = 0; i < size; i++)
            {
                array[i] = nextInt();
            }
            
            return array;
        }
        
        long[] nextLongArray(int size) 
        {
            long[] array = new long[size];
            
            for (int i = 0; i < size; i++)
            {
                array[i] = nextLong();
            }
            
            return array;
        }
        
        BigInteger nextBigInteger() 
        {
            return new BigInteger(next());
        }
            
        List<Integer>[] readGraph(int vertexNumber, int edgeNumber, boolean undirected)
        {
            List<Integer>[] graph = new List[vertexNumber];
                    
            for (int index = 0; index < vertexNumber; ++index)
            {
                graph[index] = new ArrayList<Integer>();
            }
                    
            while (edgeNumber-- > 0)
            {
                int from = nextInt() - 1;
                int to   = nextInt() - 1;
                        
                graph[from].add(to);
                
                if(undirected)
                    graph[to].add(from);
            }
                    
            return graph;
        }
    }

    public static void main(String[] arg) 
    {
        new A().run();
    }
}