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 convert_binary(num):
    result = []
    if num <= 1:
        result.append(num)
    else:
        while True:
            consult = num / 2
            reminder = num % 2
            result.append(reminder)

            if consult == 1:
               result.append(consult)
               break

            num = consult
    
    return result[::-1]

def add_zero(num, n):
    binary_ya = convert_binary(num)
    if len(binary_ya) < n:
        binary_ya = (n-len(binary_ya))*[0] + binary_ya
    return binary_ya

def friend(person, fedor, k):
    friend = 0
    for i in range(len(person)):
        if person[i] != fedor[i]:
            friend += 1
    if friend <= k:
        return True
    return False

n, m, k = map(int,raw_input().split())
xiaohuoban = []
for i in range(m):
    xiaohuoban.append(add_zero(int(raw_input()), n))
fedor = add_zero(int(raw_input()), n)

result = 0
for i in range(len(xiaohuoban)):
    if friend(xiaohuoban[i],fedor,k) == True:
        result += 1
print result