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:
def binaryForm(n):
    result = ''
    while n:
        result += str(n % 2)
        n //= 2
    return result


def compare(x, y):
    st1 = binaryForm(x)
    st2 = binaryForm(y)
    maxLength = max(len(st1), len(st2))
    tp = '0'
    tp1 = tp * (maxLength - len(st1))
    tp2 = tp * (maxLength - len(st2))
    st1+=tp1
    st2+=tp2
    result=0
    for i in range(maxLength):
        if st1[i]!=st2[i]:
            result+=1
    return result

n, m, k = map(int, input().split())
listNum = []
for _ in range(m):
    listNum.append(int(input()))
compareNum = int(input())

result = 0
for num in listNum:
    if compare(compareNum, num)<=k:
        result += 1
print(result)