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:
# initial strategy: 
# 1- get the binary bits difference between each player and Fedor.
# 2- if the difference is smaller than k, then count that as a friend.


n, m, k = [int(x) for x in input().split()]
players = [int(input()) for x in range(m+1)]

def difference(b1, b2):
    diff = 0
    for x in range(len(b1)): # len(b1) == len(b2)
        if b1[x] != b2[x]:
            diff += 1
    
    return diff

def fren(players, k, n):
    f = 0
    binFedor =  ('0'*( n-len(bin(players[-1])[2:]) )) + bin(players[-1])[2:]
    for p in players[:len(players)-1]:  # exclude Fedor
        # ('0'*( n-len(bin(p)[2:]) )) is to complete the left digits
        binP = ('0'*( n- len(bin(p)[2:]) ))+bin(p)[2:]
        if difference(binFedor, binP) <= k:
            f += 1
    
    return f


print (fren(players, k, n))