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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
	
	public class One1 {
		public static int comp(int x,int y,int z)
		{
			int differences = 0;
			while((x!=0)||(y!=0))
			{
				if(x%z != y%z)
				{
					differences++;
				}
				x = (int) x/z;
				y = (int) y/z;
			}
			return differences;
		}
		public static void main(String[] args)throws IOException
		{
			BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
			StringTokenizer st = new StringTokenizer(br.readLine());
			int n = Integer.parseInt(st.nextToken());
			int m = Integer.parseInt(st.nextToken());
			int k = Integer.parseInt(st.nextToken());
			int[] players = new int[m];
			for(int i = 0;i<m;i++)
			{
				players[i] = Integer.parseInt(br.readLine());
			}
			int friends = 0;
			int fedor = Integer.parseInt(br.readLine());
			for(int i = 0;i<m;i++)
			{
				if(comp(fedor,players[i],2) <= k )
					friends++;
			}
			System.out.println(friends);
	}
	}