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:
from sys import stdin
from itertools import zip_longest

n, m, k = [int(i) for i in stdin.readline().split()]


def main():
    potential_friends = []
    for i in range(m):
        potential_friends.append(bin(int(stdin.readline()))[2:][::-1])
    fedor = bin(int(input()))[2:][::-1]
    friends = 0
    for potential_friend in potential_friends:
        errors = 0
        for pair in zip_longest(fedor, potential_friend, fillvalue='0'):
            if pair[0] != pair[1]:
                errors += 1
                if errors > k:
                    break
        if errors <= k:
            friends += 1

    print(friends)


main()