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 PYTHON):

Solution:
s = raw_input().split()
n = int(s[0])
m = int(s[1])
k = int(s[2])
j = []
friends = 0
for i in range(0, m+1):
	x = int(raw_input())
	s = ""
	f = ""
	while x != 1:
		s += `x%2`
		x /=2

	for i in range(0, n-len(s)-1):
		f += '0'
	s1 = '1' + s[::-1]
	j += [f+s1]

for i in j[:-1]:
	count = 0
	c1 = 0
	while count < n:
		if i[count] != j[-1][count]:
			c1 += 1
		count += 1

	if c1 <= k:
		friends +=1

print friends