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())

arr = []

for i in range(m+1):
    arr.append(int(input()))
    
v,y = "",arr[-1]

while y != 0:
    
    v += str(y % 2)
    
    y //= 2
    
h,v,ans = m-1,v[::-1],0

while h >= 0:
    
    f,t = arr[h],""
    
    while f != 0:
        
        t += str(f % 2)
        
        f //= 2
        
    n1,n2,t = len(t),len(v),t[::-1]
    
    if n1 > n2:
        
        v = "0"*(n1-n2) + v
        
    elif n1 < n2:
        
        t = "0"*(n2-n1) + t
        
    c = 0
        
    for i,j in enumerate(v):
        
        if j != t[i]:
            
            c += 1
            
    if c <= k:
        
        ans += 1
        
    h -= 1
print(ans)