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:
string = input()
numbers = string.split(" ")
types = int(numbers[0])
players = int(numbers[1])
armies = int(numbers[2])
binaries = []
for x in range(players + 1):
    army = int(input())
    binary = ""
    while army != 0:
        binary += str(army % 2)
        army = int(army / 2)
    binary += "0" * (types - len(binary))
    binary = binary[::-1]
    binaries.append(binary)
player = binaries[players]
friends = 0
for x in range(players):
    differences = 0
    for y in range(types):
        if binaries[x][y] != player[y]:
            differences += 1
    if differences <= armies:
        friends += 1
print(friends)