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, stdout, setrecursionlimit
input = stdin.readline
flush = stdout.flush

#setrecursionlimit(1000000)

############################################################

OUT = []

def write(item, sep = " "):
    if type(item) is int:
        OUT.append(str(item))
    elif type(item) is list:
        if type(item[0]) is int:
            OUT.append(sep.join(map(str, item)))
        else:
            OUT.append(sep.join(item))
    else:
        OUT.append(item)

def PRINT():
    print("\n".join(OUT))

GI = lambda: int(input())
GS = lambda: input()[:-1]

gi = lambda: list(map(int, input().split()))
gs = lambda: input().split()

############################################################

n, m, k = gi()

friends = []

for i in range(m):
    a = GI()
    friends.append(a)

fedor = GI()
y = 0

for i in friends:
    i ^= fedor
    if bin(i).count("1") <= k:
        y += 1

write(y)

PRINT()