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:
nmk = raw_input();
[n,m, k] = nmk.split();
m = int(m);
n = int(n);
k = int(k);

def dist(s, t):
  d = 0;
  for i in range(len(s)):
    if s[i]<>t[i]:
      d = d+1;
  return d;

x = [];
b = [];
for i in range(m+1):
  x.append(int(raw_input()));
  bn = bin(x[i]);
  bn = bn[2:];
  while len(bn)<n:
    bn = '0'+bn;
  b.append(bn);

#print b

r = 0;
for i in range(m):
  if (dist(b[i],b[m])<=k):
    r = r+1;
    
print r