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.*;
public class Soldier {
    public static void main(String[] args) throws IOException{
		BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
		String line = null;
	    line = bf.readLine();
	    String[] str = line.split(" ");
	    int n = Integer.parseInt(str[0]);
	    int m = Integer.parseInt(str[1]);
		int k = Integer.parseInt(str[2]);
		
		int[] soldiers = new int[m];
		for(int i=0; i<m; i++){
			line = bf.readLine();
			soldiers[i] = Integer.parseInt(line);
		}
		
		line = bf.readLine();
		int fedor = Integer.parseInt(line);
		
		int count = 0;
		int mask = 1;
		for(int i=0; i<m; i++){
			int diff = 0;
			int interval = fedor^soldiers[i];
			for(int j=0; j<n; j++){
				if((mask&(interval>>j))==1) diff++;
			}
			if (diff <= k) count++;
			//System.out.println(i+" "+count);
		}
		System.out.println(count);
	}
}