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 PYTHON):

Solution:
from __future__ import division
from collections import Counter as ctr
from math import ceil, log, factorial, sqrt
# reads a line of input and converts into a list of ints
# 1 1 3 => [1, 1, 3]
def rl():
    return [int(i) for i in raw_input().split()]

# reads n lines of input (if n defined) and returns a list of strings
# where each element is a line in the input
# abc
# abcdef
# => ['abc', 'abcdef']
# if n not defined, read first line to get number of lines
# 2
# abc
# abcdef
# => ['abc', 'abcdef']
def rm(n=None):
    if n is None:
        n = input()
    return [raw_input() for i in range(n)]

# same as rm, except converts each line to a list of ints like rl
def rlm(n=None):
    if n is None:
        n = input()
    return [rl() for i in range(n)]

def yn(b):
    if b:
        print "YES"
    else:
        print "NO"

n, m, k = rl()
players=[i[0] for i in rlm(m)]
fedor=int(raw_input())
match=0
for i in players:
    dif = bin(fedor ^ i)[2:].count('1')
    if dif <= k:
        match += 1
print match