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:
'''input
3 3 3
1
2
3
4
'''
from sys import stdin, stdout
import math


def compute_diff(marr, cur, n):
	temp = '0'* (n - len(marr[cur])) + marr[cur]
	diff = 0
	for i in range(n):
		if marr[-1][i] != temp[i]:
			diff += 1
	return diff


# main starts
n, m, k  = list(map(int, stdin.readline().split()))
marr = []
for i in range(m + 1):
	marr.append(int(stdin.readline().strip()))

for i in range(m + 1):
	marr[i] = str(bin(marr[i]))[2:]

marr[-1] = '0' * (n - len(marr[-1])) + marr[-1]

friends= 0
for i in range(m):
	diff = compute_diff(marr, i, n)
	if diff <= k:
		friends += 1

print(friends)