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;

public class Main {
public static void main(String[] args) {
	Scanner s = new Scanner(System.in);
	int type=s.nextInt(),noOfOtherPlayers=s.nextInt(),upprLimit=s.nextInt();
	int arr[]=new int[noOfOtherPlayers];
	for(int i=0;i<arr.length;i++){
		arr[i]=s.nextInt();
	}
	int player=s.nextInt();
	int friends=0;
	for(int i=0;i<arr.length;i++){
		if(isFriend(player, arr[i], upprLimit)){
			friends++;
		}
	}
	System.out.println(friends);
	s.close();
}

public static boolean isFriend(int player,int oplayer,int k){
	String p=Integer.toString(player, 2),op=Integer.toString(oplayer,2);
	int nonMatching=0,i,j;
	for(i=p.length()-1,j=op.length()-1;i>=0&&j>=0;i--,j--){
		if(p.charAt(i)!=op.charAt(j)){
			nonMatching++;
		}
	}
	while(i>=0){
		if(p.charAt(i--)=='1')
			nonMatching++;
	}
	while(j>=0){
		if(op.charAt(j--)=='1')
			nonMatching++;
	}
	if(nonMatching>k)
		return false;
	else return true;
}
}