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:
import itertools;

def dCount( a, b):
	c = a ^ b;
	d = 0;
	while(c>0):
		if(c & 1):
			d+=1;
		c/=2;
	return d;

firstLine = map(int, raw_input().split());
types = firstLine[0];
m = firstLine[1];
k = firstLine[2];

players = [];

for i in range(0, m+1):
	players.append(int(raw_input()));
	
fedor = players[-1];
friends = 0;

for i in range(0, len(players)-1):
	if(dCount(players[i], fedor)<=k):
		friends+=1;

print(friends);

'''valids = [fedor];
flips = [];
starter = [];
flipInt = 0;


for i in range(1, k+1):
	starter = [];
	for j in range(0, types):
		starter.append(0);
	for j in range(0, i):
		starter[j] = 1;
	#print(starter);
	flips = list(set(itertools.permutations(starter)));
	
	#print(flips);
	
	
	for a in flips:
		flipInt = 0;
		for b in range(0, len(a)):
			if(a[b]==1):
				flipInt += 2**b;
		#print a, flipInt;
		valids.append( fedor ^ flipInt);
		
#print(valids);
friends = 0;
		
for i in range(0, len(players)-1):
	if(players[i] in valids):
		friends += 1;
print friends;'''