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 sys

def plist(a, s = ' ') :
  print s.join(map(str, a))

def rint() :
  return int(sys.stdin.readline())

def rints() :
  return map(int, sys.stdin.readline().split())

n, m, k = rints()

def digits(x, p) :
  digits = []
  while x > 0 :
    digits.append(x % p)
    x /= p
  return digits
   
x = []
for i in range(m + 1) :
  d = digits(rint(), 2)
  x.append(d + [0] * (n - len(d)))

friends = 0
fedor = x[-1]

for guy in x[:-1] :
  delta = sum([a != b for a, b in zip(guy, fedor)])
  if delta <= k :
    friends += 1

print friends