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:
"""
Oh, Grantors of Dark Disgrace, 
Do Not Wake Me Again.
"""

# import stackprinter
# stackprinter.set_excepthook(style='color')

ii = lambda: int(input())
mi = lambda: map(int, input().split())
li = lambda: list(mi())
si = lambda: input()

def baseb(n, b):
    q, r = divmod(n, b)
    if n == 0:
        return '0'
    elif q == 0:
        return str(r)
    else:
        return baseb(q, b) + str(r)

n, m, k = mi()
s = [0]*(m+1)

for i in range(m+1):
    f = baseb(ii(), 2)
    lf = len(f)
    s[i] = (n-lf)*'0' + f if lf < n else f

print(sum(sum(int(y)^int(u) for y, u in zip(i, s[-1])) <= k for i in s)-1)