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 PYTHON3):

Solution:

def decToBin(x):
 	return (bin(x)[2:])

def compare(x, y):
	check = 0;
	alpha = list(decToBin(x));
	beta = list(decToBin(y));
	count = 0;

	for i in range (len(alpha), a[0]):
		alpha.insert(0,"0");
	for i in range (len(beta), a[0]):
		beta.insert(0,"0");
	for j in range (0, a[0]):
			if (alpha[j] != beta[j]):
				count += 1;
	if (count <= a[2]):
		check = 1;
	return check;


b = [];
g_count = 0;
a = [int(x) for x in input().split()]
for i in range (0, a[1] + 1):
	b.append(int(input()));

for i in range (0, a[1]):
	g_check = compare(b[i], b[a[1]]);
	if (g_check == 1):
		g_count += 1;

print (g_count);