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:
import time
import collections

class Time_test:
    def __enter__(self):
        self.enter_time = time.time()
    def __exit__(self, exc_type, exc_val, exc_tb):
        print("Command was executed in", time.time()-self.enter_time)

n, m, k = [int(x) for x in input().split()]
arr = []
for i in range(m):
    tmp = bin(int(input()))[2:]
    arr.append('0'*(n-len(tmp)) + tmp)

fedya = bin(int(input()))[2:]
fedya = '0'*(n-len(fedya)) + fedya

c = 0
for i, elem in enumerate(arr):
    counter = 0
    for j, e in enumerate(elem):
        if e != fedya[j]:
            counter += 1
    if counter <= k:
        c += 1

print(c)