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:
###################################
## Eric Breno B. - UFCG - BRAZIL ##
###################################

a, b, c = map(int, raw_input().split())

ns = []
coms = {}

for i in xrange(b+1):
	ns.append(int(raw_input()))
	coms[ns[-1]] = 9999999999999999
	
mn = bin(ns[-1])[2:]
ns.pop(-1)

def ver(n, mn):
	diffs = 0
	
	if coms[n] <= c: return True
	if coms[n] > c and coms[n] != 9999999999999999: return False
	
	nn = bin(n)[2:]
	if len(nn) > len(mn): mn = '0'*len(nn) + mn
	else: nn = "0"*(len(mn)) + nn
	
	for i in xrange(min(len(mn), len(nn))):
		if mn[-1-i] != nn[-1-i]:
			diffs += 1

	coms[n] = diffs
	
	if coms[n] <= c: return True	
	return False

amgs = 0
for i in ns:
	if ver(i, mn): 
		amgs += 1
	
	
print amgs