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 main
{
	public static void main(String[] args) throws Exception
	{
		BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));

		String[] nmk = reader.readLine().split(" ");

		int n = Integer.parseInt(nmk[0]);
		int m = Integer.parseInt(nmk[1])+1;
		int k = Integer.parseInt(nmk[2]);

		int[] soldiers = new int[m];

		for(int i=0;i<m;i++)
			soldiers[i] = Integer.parseInt(reader.readLine());


		int count = 0;
		for(int i=0;i<m-1;i++)
		{
			int xor = soldiers[i] ^ soldiers[m-1];

			String seq = Integer.toString(xor,2);
			
			int x =0;
			for(int j=0;j<seq.length();j++)
			{
				if(seq.charAt(j) == '1')
					x++;
			}

			if(x <= k)
				count++;
		}

		System.out.println(count);
	}
}