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 pad_number(number, number_of_bits):
    if len(number) == number_of_bits:
        return number
    elif len(number) > number_of_bits:
        raise Exception("Number is larger than number of bits.")

    while len(number) != number_of_bits:
        number = '0' + number

    return number

def get_diff(number1, number2, n):
    diff = 0
    for i in xrange(n):
        if number1[i] != number2[i]:
            diff += 1

    return diff

def get_potential_friends(n, m, k, args=None):
    args = [pad_number(number, n) for number in args]
    fedor, friends = args[-1], 0
    for arg in args[:-1]:
        if get_diff(arg, fedor, n) <= k:
            friends += 1

    return friends

if __name__ == "__main__":
    inpt = raw_input()
    args = [int(el) for el in inpt.split(' ')]
    add_args = [bin(int(raw_input()))[2:] for i in xrange(args[1] + 1)]
    rtn = get_potential_friends(*args, args=add_args)
    if type(rtn) is list:
        for el in rtn:
            print el

    else:
        print rtn