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 check_differ(teammate,fedor,differ_limit):
    match=True
    differ_count=0
    for i in range(0, len(teammate)):
        if teammate[i] != fedor[i]:
            differ_count +=1
        if differ_count > differ_limit:
            match=False
            break
    return match

if __name__ == "__main__":
    solder_types,teammates,differ_limit = map(int,input().split())
    player=[None]*(teammates+1)
    friends=0
    for i in range(len(player)):
        player[i]=bin(int(input()))[2:].zfill(solder_types)
    for i in range(len(player)-1):
        if check_differ(list(bit for bit in player[i]),list(bit for bit in player[-1]),differ_limit) :
            friends += 1
    print(friends)