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.FileNotFoundException;
import java.util.Scanner;

public class Main
{
    static int countOnes(int num, int n)
    {
	int count = 0;
	for (int i = 0; i < n; i++)
	{
	    if ((num & 1) == 1)
		count++;
	    num /= 2;
	}

	return count;
    }

    public static void main(String[] args) throws FileNotFoundException
    {
	Scanner sc = new Scanner(System.in);

	int n, m, k;
	n = sc.nextInt();
	m = sc.nextInt() + 1;
	k = sc.nextInt();

	int[] player = new int[m];
	for (int i = 0; i < m; i++)
	    player[i] = sc.nextInt();

	int count = 0;
	for (int i = 0; i < m - 1; i++)
	{
	    if (countOnes((player[m - 1] ^ player[i]), n) <= k)
		count++;
	}

	System.out.println(count);

	sc.close();
    }
}