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 binario(n):
  return bin(n)[2:]

def canBecomeFriends(number, limit, tamMax):
  # = tamMax - len(number)
  uns = 0
  if uns > limit:
    return False
  for i in range(len(number)):
    if number[i] == '1':
      uns += 1
    if uns > limit:
      return False
  return True

n, m, k = map(int, input().split())
#players 1 até m + 1
#type 0 até n - 1

armys = []
bins = []
for i in range(m + 1):
  army = int(input())
  #army = binario(army)
  armys.append(army)
  #bins.append(binario(army))

#print(armys)
#print(bins)
fedorsArmy = armys[-1]
friends = 0
#print('k ' + str(k))
for i in range(m):
  bitwise = (armys[i] ^ fedorsArmy)
  tamMax = len(binario(max(armys[i], fedorsArmy)))
  #print('tamMAx ' + str(tamMax))
  bitwise = binario(bitwise) 
  #print('bitwise: ' + bitwise)
  if canBecomeFriends(bitwise, k, tamMax):
    friends += 1

print(friends)