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.math.BigInteger;
import java.util.*;
import java.io.*;
 
public class Main {
   public static void main(String[] args) {
      // Use the Scanner class
      Scanner sc = new Scanner(System.in);  

      int n=sc.nextInt();
      int m=sc.nextInt();
      int k=sc.nextInt();

      String[] playersBinary = new String[m+1];
      for (int i = 0; i < m+1; i++) {
         int number = sc.nextInt();

         String strBinaryNumber = Integer.toBinaryString(number);

         String pad = String.format("%0"+n+'d',0);
         strBinaryNumber = pad.substring(strBinaryNumber.length()) + strBinaryNumber;

         playersBinary[i] = strBinaryNumber;
      }

      int totalFriends = 0;
      for (int i = 0; i < playersBinary.length-1; i++) {
         int differences = 0;
         boolean canBeFriends = true;
         for (int j = 0; j < n; j++) {
            char fedorType = playersBinary[m].charAt(j);
            char foeType = playersBinary[i].charAt(j);

            if (fedorType != foeType) {
               differences++;

               if (differences > k) {
                  canBeFriends = false;
                  break;
               }
            }
         }

         if (canBeFriends) {
            totalFriends++;
         }
      }

      System.out.println(totalFriends);
   }
}