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:
n,m,k=map(int, input().split())

bin_len=[]
bins=[]
diff=0
ans=0

for _ in range(m):
  bins.append(bin(int(input()))[2:])
  bin_len.append(len(bins[-1]))

fedor=bin(int(input()))[2:]
fedor_len=len(fedor)

for i in range(m):
  diff=0
  for j in range(-1,-n-1,-1):
    if j<-fedor_len:
      d1="0"
    else:
      d1=fedor[j]

    if j<-bin_len[i]:
      d2="0"
    else:
      d2=bins[i][j]
    
    if d1!=d2:
      diff+=1
      if diff>k:
        break

  else:
    ans+=1
  
print(ans)