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.Scanner;
import java.lang.Math;
public class b467
{
   public static void main(String args[])
   {
      Scanner ssj = new Scanner(System.in);
      
      int n = ssj.nextInt();
      int m = ssj.nextInt();
      int k = ssj.nextInt();
      
      int arr[] = new int[m + 1];
      
      for(int i = 0; i <= m; i++)
      {
         arr[i] = ssj.nextInt();
      }
      
      int friends = 0;
      
      for(int i = 0; i < m; i++)
      {
         //System.out.println("arr[" + i + "] = " + arr[i]);
         //System.out.println("arr[m] = " + arr[m]);
         int countDiffer = countOne(arr[i], arr[m]);
         //System.out.println("countDiffer = " + countDiffer);
         if(countDiffer <= k)
         {
            friends++;
         }
      }
      
      System.out.println(friends);
   }
   
   static int countOne(int x, int y)
   {
      String m = Integer.toBinaryString(x);
      //System.out.println("m = " + m);
      String n = Integer.toBinaryString(y);
      //System.out.println("n = " + n);
      
      int ans = 0;
      
      if(m.length() == n.length())
      {         
         for(int i = 0; i < m.length(); i++)
         {
            char a = m.charAt(i);
            char b = n.charAt(i);
            
            if(a != b)
            {
               ans++;
            }           
         }        
      }
      
      else if(m.length() > n.length())
      {
         int zero = m.length() - n.length();
         String s = "";
         for(int i = 0; i < zero; i++)
         {
            s += "0";
         }
         n = s + n;
         
         for(int i = 0; i < m.length(); i++)
         {
            char a = m.charAt(i);
            char b = n.charAt(i);
            
            if(a != b)
            {
               ans++;
            }           
         }           
      }
      
      else //n.length() > m.length()
      {
         int zero = n.length() - m.length();
         String s = "";
         for(int i = 0; i < zero; i++)
         {
            s += "0";
         }
         m = s + m;
         
         for(int i = 0; i < n.length(); i++)
         {
            char a = m.charAt(i);
            char b = n.charAt(i);
            
            if(a != b)
            {
               ans++;
            }           
         }           
      }
      return ans;
   }
}