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:
def to_binary(number):
    result = []
    if number <= 1:
        result.append(number)
    else:
        while True:
            quotient = number / 2
            reminder = number % 2
        
            result.append(reminder)
            if quotient == 1:
                result.append(1)
                break
            else:
                number = quotient
    return result

def to_binary_in_length(number, length):
    result = to_binary(number)[::-1]

    if len(result) < length:
        return ([0] * (length - len(result))) + result
    else:
        return result

def cal_difference(others, fedor):
    result = 0
    for i in range(len(fedor)):
        if others[i] != fedor[i]:
            result += 1
    return result

players = []

binary_length, m, allowed_difference = map(int, raw_input().split())
for i in range(m):
    players.append(to_binary_in_length(int(raw_input()), binary_length))
fedor = to_binary_in_length(int(raw_input()), binary_length)

result = 0
for i in range(m):
    if cal_difference(players[i], fedor) <= allowed_difference:
        result += 1
print result