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:
'''
Fedor and New Game

time limit per test: 1 second
memory limit per test: 256 megabytes
input: standard input
output: standard output

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.


'''

def main():
    n,m,k = map(int,input().split(' '))

    x = []
    for _ in range(m+1):
        x.append(int(input()))

    friendsCount = 0
    for i in range(m):
        # xor operation to get the differences in bits between numbers
        if bin(x[m] ^ x[i]).count('1') <= k:
            friendsCount += 1

    print(friendsCount)

if __name__ == "__main__":
    main()