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 calculate_types_of_army(bit_army):
    types = 0
    while bit_army != 0:
        bit_army //= 10
        types += 1

    return types


def add_zeros(bin_repr, n):
    while len(bin_repr) < n:
        bin_repr = '0' + bin_repr

    return bin_repr


def calculate_friends(bitmask, Fedor_army, bin_repr):
    friends = 0
    for army in bitmask:
        army_variation = 0
        for bit in range(len(army)):
            if army[bit] != Fedor_army[bit]:
                army_variation += 1
        if army_variation <= bin_repr:
            friends += 1

    return friends


types_of_soldiers, num_of_players, bin_repr = [int(i) for i in input().split()]

player_army = []    # integer repr of army
bit_masks = []      # binary repr of army
for _ in range(num_of_players + 1):
    player_army.append(int(input()))

bit_masks = [add_zeros(str(bin(i)[2:]), types_of_soldiers) for i in player_army]
Fedor_army = bit_masks[-1]
bit_masks.pop() # remove fedor's army

friends = calculate_friends(bit_masks, Fedor_army, bin_repr)

print(friends)