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:
num = list (map (int ,  input().split() ))
n , m , k = num[0] , num[1] ,num[2]
# print(m)
players=[]
for _ in range (m):
    players.append(int(input()))
fed = int(input())
# print(players)
fedtr = format(fed , '#0' + str(n+2) +'b')[2:]
# print(fedtr)
total =0 
for i in players:
    tempstr = format(i , '#0' + str(n+2) +'b')[2:]
    u = zip(fedtr,tempstr)
    count =0
    for i,j in u:
        if (i!=j):
            count = count + 1
    
    if(count<=  k ):
        total = total+1

print(total)