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 main():
    s = input().split()
    n = int(s[0])
    m = int(s[1])
    k = int(s[-1])
    players = []
    for i in range(m):
        player = int(input())
        players.append(player)
    fedor = int(input())
    army = []
    for i in range(n):
        army.append(fedor%2)
        fedor = fedor // 2
    output = 0
    for i in range(m):
        dif = 0
        j = 0
        t = 0
        while j < len(army) and t<n:
            if players[i] % 2 != army[j]:
                dif += 1
            j += 1
            players[i] = players[i] //2
            t += 1
        if dif <= k:
            output += 1
    print(output)
            
main()