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:
# python 3
"""
"""


def count_set_bits(n_int):
    count = 0
    while n_int:
        count += n_int & 1
        n_int >>= 1
    return count


def fedor_and_new_game(m_int, k_int, players_list) -> int:
    fedor = players_list[-1]
    friends = 0
    for i in range(m_int):
        player = players_list[i]
        if count_set_bits(player ^ fedor) <= k_int:
            friends += 1
    return friends


if __name__ == "__main__":
    """
    Inside of this is the test. 
    Outside is the API
    """
    n, m, k = list(map(int, input().split()))
    players = [int(input()) for i in range(m+1)]

    print(fedor_and_new_game(m, k, players))