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.util.Arrays;
//import java.util.Math;
public class mitul
{
       public static void main(String args[])
       {
            
            Scanner scan = new Scanner(System.in);
            int n = scan.nextInt();
            int m = scan.nextInt();
            int k = scan.nextInt();
            int count=0,count1=0,FLAG=0;
            int[] arr = new int[m+1];
            String[] arr1 = new String[m+1];
            String[] str = new String[m+1];
            for(int i=0;i<=m;i++)
            {
                   arr[i]=scan.nextInt();
            }
            for(int i=0;i<=m;i++)
            {
                arr1[i]=Integer.toBinaryString(arr[i]);
                StringBuffer str1 = new StringBuffer(arr1[i]);
                while(str1.length()!=n)
                {
                       str1.insert(0,'0');
                }
                
                str[i]=str1.toString();
            }
            
            
            String mylord=str[m];
            for(int i=0;i<m;i++)
            {
                   FLAG=0;
                   count=0;
                   for(int j=0;j<mylord.length();j++)
                   {
                   if(str[i].charAt(j)!=mylord.charAt(j))
                   {
                          count++;
                   }
                   if(count>k)
                   {
                          FLAG=1;
                          break;
                   }
                   }
                   if(FLAG==1)
                   {
                          count1++;
                   }
            }
           // System.out.println(count1);
            System.out.println(m-count1);
       }
}