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:
n, m, k = map(int, input().split())
a = []
for i in range(m+1):
    a.append(format(int(input()), 'b')[::-1])
t = a.pop()
l = len(t)
f = 0
for i in a:
    c = 0
    x = 0
    for j in range(min(l, len(i))):
        if t[j] != i[j]:
            c += 1
        if c > k:
            x = 1
            break
    if len(i) < l:
        c += (t[len(i):]).count('1')
    if len(i) > l:
        c += (i[l:]).count('1')
    if c > k:
        x = 1
    if x != 1:
        f += 1
print(f)


'''
8  - 1000
17 - 1001

5  - 0101


'''