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:
n, m, k = map(int, raw_input().split())
t = m
li = []
li2 = [0] * n

def com(z):
    p = n -1
    cnt = 0
    while p >= 0:
        if z % 2 != li2[p]:
            cnt += 1
        z /= 2
        p -= 1
    return cnt
while t >= 0:
    x = input()
    li.append(x)
    t -= 1
fedor = li[m]
i = n -1
while fedor != 0:
    li2[i] = fedor % 2
    i -= 1
    fedor /= 2
i = 0
res = 0
while i < m:
    if com(li[i]) <= k:
        res += 1
    i += 1
print(res)