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 sys, os
# import numpy as np
from math import sqrt, gcd, ceil, log, floor
from bisect import bisect, bisect_left
from collections import defaultdict, Counter, deque
from heapq import heapify, heappush, heappop
from itertools import permutations
input = sys.stdin.readline
read = lambda: list(map(int, input().strip().split()))
# read_f = lambda file:  list(map(int, file.readline().strip().split()))
# from time import time
# sys.setrecursionlimit(5*10**6)

MOD = 10**9 + 7

def f(x, y):
	x ^= y
	c = 0
	while x:
		c += 1
		x &= x-1
	return(c)


def main():
	# file1 = open("C:\\Users\\shank\\Desktop\\Comp_Code\\input.txt", "r")
	# n = int(file1.readline().strip()); 
	# arr = list(map(int, file1.read().strip().split(" ")))
	# file1.close()
	# n = int(input())
	n, m, k = read(); arr = []
	for i in range(m+1):
		arr.append(int(input()))
	m_1 = arr[-1]
	ans = 0
	for i in range(m):
		ans += k >= f(m_1, arr[i])
	print(ans)



	# file = open("output.txt", "w")
	# file.write(ans+"\n")
	# file.close()

if __name__ == "__main__":
	main()

"""

"""