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 fractions import Fraction as F
import math
import sys

fi = sys.stdin
fo = sys.stdout
fe = sys.stderr
exit = sys.exit

readline = raw_input

def readargs(tp=None):
	if tp is not None:
		return map(tp, readline().split())
	return readline.split()

def yesno(flag, yes='', no=''):
	if flag:
		print yes if yes else 'YES'
	else:
		print no if no else 'NO'

truefalse = lambda flag : yesno(flag, yes='TRUE', no='FALSE')

def binary_cnt(who):
    return bin(who).count('1')

n, m, k = readargs(int)
armys = [int(readline()) for _ in range(m)]
mine = int(readline())
cnt = 0
for army in armys:
    if binary_cnt(mine ^ army) <= k:
        cnt += 1

print cnt