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:
'''input
3 3 3
1
2
3
4
'''



def dec_to_bin(x):
    return bin(x)[2:]


def checkDiff(p1, p2, n, k):
    d1 = n - len(p1)
    d2 = n - len(p2)

    if d1 > 0:
        p1 = '0'*d1 + p1 

    if d2 > 0:
        p2 = '0'*d2 + p2 


    diff = 0
    # print(p1, p2, "  player  ")
    for i in range(n):
        if p1[i] != p2[i]:
            diff += 1


    if diff > k:
        return 0
    else:
        # print("matched", p1, p2, diff)
        return 1

def main():

    n, m, k = map(int, input().split())

    players = []
    for i in range(m):
        players.append(int(input()))



    mainPlayer = int(input())
    
    count = 0
    for i in players:
        if(checkDiff(dec_to_bin(mainPlayer), dec_to_bin(i), n, k)):
            count += 1

    print(count)


if __name__ == "__main__":
    main()