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:
n,m,k = map(int,raw_input().split())
x = []
for i in range(m+1):
	xi = input()
	x.append(xi)
_fedor = x[-1]
_Fedor_bin = bin(_fedor)[2:]
_Fedor_bin = '0'*(n - len(_Fedor_bin)) + _Fedor_bin
_Fedor_dic = {i:j for i,j in enumerate(_Fedor_bin)}
#print _Fedor_dic
counter = 0
for xi in x[:len(x) -1]:
	_bin = bin(xi)[2:]
	_bin = '0'*(n - len(_bin)) + _bin
	_dic = {i:j for i,j in enumerate(_bin)}
	#print len(_Fedor_dic), len(_dic)
	diff = 0
	for key,value in _dic.iteritems():
		if value != _Fedor_dic[key]:
			diff += 1
	if diff <= k:
		counter += 1
print counter