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:
# Description of the problem can be found at http://codeforces.com/problemset/problem/467/B

# gets the numbers of bits that differ between "a" and "f"
def get_diff(a, f):
    s = 0

    while a != 0 or f != 0:
        a_b = a % 2
        f_b = f % 2
        a //= 2
        f //= 2
        if a_b != f_b:
            s += 1
    
    return s


n, m, k = map(int, input().split())
l = list()

for _ in range(m):
    l.append(int(input()))
f = int(input())

s = 0
for i in l:
    s += 1 if get_diff(i, f) <= k else 0
print(s)