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:
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		Scanner sc=new Scanner(System.in);
		int i=0,j=0,k=0;
		int n=sc.nextInt();         //types of army
		int m=sc.nextInt();        //fedor is (m+1)th player
		int bits=sc.nextInt();          //atmost bits to be friend
		int counter=0;
		int friend=0;
		int quo=0;
		int remainder=0;
		ArrayList<Integer> rem= new ArrayList<Integer>();
		
		int[] army=new int[m+1];
		int[] fedorbits=new int[n];
		
		
		int[] armybits=new int[n];
		for(i=0;i<m+1;i++)
		{
		    army[i]=sc.nextInt();
		}
		
		
		
		int fedor=army[m];
		quo=fedor;
		while(quo!=1)
		{
		    fedor=quo;
		    rem.add(fedor%2);
		    quo=fedor/2;
		}
		rem.add(1);
		int size=rem.size();
		while(size!=n)
		{
		    rem.add(0);
		    size=rem.size();
		}
		Collections.reverse(rem);
		//System.out.println(rem);
		int index=0;
		int duparmy=0;
		friend=m;
		for(i=0;i<m;i++)
		{
		    index=n;
		    counter=0;
		    duparmy=army[i];
		    quo=army[i];
		    for(j=0;j<n;j++)
		    {
		        duparmy=quo;
		        remainder=duparmy%2;
		        quo=duparmy/2;
		        //System.out.println("player : index "+i+" : "+j+" ::: remainder :  "+remainder);
		        if(remainder!=rem.get(index-1))
		        {
                   
		            counter++;
		             //System.out.println("Discrepancy : Checking player : "+ i +"  and index: "+ j+ "  Remainder of player vs fedor  :: "+ remainder +" ::: "+rem.get(index-1) );
		        }
		        index--;
		        if(counter>bits)
		        {
		            //System.out.println("removed player is "+ i);
		            friend--;
		            break;
		        }  
		 }
		    
		}
		
		
		
		System.out.println(friend);
		
	}
}