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.*;
import java.io.PrintWriter;

public class B467 implements Runnable {
	private Scanner in = new Scanner(System.in);
	private PrintWriter out = new PrintWriter(System.out);
	private int n;
	private int m;
	private int k;
	private int a[];
	private int b[];
	private int ans=0;
	
	public static void main(String[] args) {
		new Thread(new B467()).start();
	}

	private void read() {
		n = in.nextInt();
		m = in.nextInt();
		k = in.nextInt();

		a = new int[m+1];
		b = new int[m+1];

		String temp = "";
		for(int i = 0; i <= m; i++) {
				a[i] = in.nextInt();
		}

	}

	private void solve() {
		String temp;
		int count = 0;
		for(int i = 0; i < m; i++) {
			temp = Integer.toBinaryString(a[i]^a[m]);
			for(int j = 0; j < temp.length(); j++){
				if(temp.charAt(j) == '1'){
					count++;
				}
			}
			if(count <= k){
				ans++;
			}
			count = 0;
			
		}
		
	}


	private void write() {
		
		out.println(ans);
		
	}


	public void run() {
		read();
		solve();
		write();
		out.close();
	} 
}