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:
"""
by goyal-aman
https://codeforces.com/problemset/problem/467/B
"""

def isFriend(friends_army, fedors_army):
    match = friends_army ^ fedors_army
    return sum([int(i) for i in bin(match) if i == '1'])

if __name__ == "__main__":
    num_friends = 0
    n,m,k = map(int, input().split())
    all_armies = []
    for _ in range(m):
        all_armies.append(int(input()))

    fedors_army = int(input())
    # print(all_armies, fedors_army)
    for army in all_armies:
        match = isFriend(army, fedors_army)
        if match<=k:
            num_friends += 1
    print(num_friends)