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 diff(a, b):
    length = 0
    d = 0
    
    if len(a) > len(b):
        b = '0'*(len(a)-len(b)) + b
        length = len(a)
    else:
        a = '0'*(len(b)-len(a)) + a
        length = len(b)
    
    for i in range(0, length):
        if a[i] != b[i]:
            d = d+1
    
    return d

[n, m, k] = [int(x) for x in input().split()]
friends = []
for i in range(0, m):
    friends.append("{0:b}".format(int(input())))

fedor = "{0:b}".format(int(input()))
ans = 0

for i in range(0, m):
    mydiff = diff(fedor, friends[i])
    if mydiff <= k:
        ans=ans+1

print(ans)