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:
var main = function(content, noMore)
{
	var nearToBinary = function(num, countIn)
	{
		if (num === 0) return countIn;
		else
			{
				if (num % 2 === 1) countIn++;
				return nearToBinary(Math.floor(num / 2), countIn);
			}
	}
	var computeSoldiers, count = 0, result = 0;
	for (var i = 0; i < content.length - 1; i++)
	{
		computeSoldiers = content[content.length - 1] ^ content[i];
		computeSoldiers = nearToBinary(computeSoldiers, count);
		
		if (computeSoldiers <= noMore) result++;
		count = 0;
	}
	return result;
}

{
	var input = readline(),
	arrContent = [],
	n,
	m,
	k;
	input = input.split(' ');
	n = +input[0];
	m = +input[1];
	k = +input[2];
	for (var i = 1; i <= m + 1; i++)
	{
		arrContent.push(+readline());
	}
	print(main(arrContent, k));
	
}