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.io.PrintWriter;
import java.util.*; 

public final class training{
	
	
	
	
	public static void main(String[] args) {
		
		int diffCounter=0,friendsCounter=0,n,m,k;
		Vector<Integer> players=new Vector<Integer>();
		Scanner in=new Scanner(System.in);		
		//PrintWriter out=new PrintWriter(System.out,true);
		//input loop
		n=in.nextInt();
		m=in.nextInt();k=in.nextInt();
		int x,y,j=0;
		for(int i=0;i<=m;i++)
		{
			x=in.nextInt();players.add((Integer)x);
		}
		//our main logic
		for(int i=0;i<m;i++){
			j=0;diffCounter=0;
			while(diffCounter<=k && j<n){
				x=players.get(i).intValue()& (1<<j);
				y=players.get(m).intValue()&(1<<j++);
				if(x!=y) diffCounter++;
				
				}
			if (diffCounter<=k)
				friendsCounter++;
		}
		System.out.println(friendsCounter);
	}

 
 }