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:
import collections
mas = []


def bit(x):
    ans = []
    while x != 1:
        ans.append(x % 2)
        x //= 2
    ans.append(x)
    ans = ans[::-1]
    return ans

n, m, k = map(int, input().split())
for i in range(m):
    x = int(input())
    mas.append(bit(x))
plus = int(input())
plus = bit(plus)
max = 0
answer = 0
for i in mas:
    if len(i) > max:
        max = len(i)
if len(plus) > max:
    max = len(plus)
for i in range(len(mas)):
    mas[i] = mas[i][::-1]
    for j in range(max - len(mas[i])):
        mas[i].append(0)
    mas[i] = mas[i][::-1]
plus = plus[::-1]
for j in range(max - len(plus)):
        plus.append(0)
plus = plus[::-1]
answer = 0
for i in mas:
    ans = 0
    for j in range(len(i)):
        if i[j] != plus[j]:
            ans += 1
    if ans <= k:
        answer += 1
print(answer)