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:
'''                      
   	
   			 ||Sri:||                 

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      |    |   ___|    |    |    ___|      |      |    |___
 /\  /\    |   |___    |    |   |___|      |      |    |___|
/  \/  \   |   ___|    |    |         |_/    |___|    |___

I am a beginner. Feel free to send tutorials/help to srinivasan1995@gmail.com.

Codeforces, SPOJ handle: desikachariar.
Hackerrank, Codechef handle: Prof_Calculus.

Advises/Help are welcome. You will definitely get a thanks in return. Comments to be avoided.

College: International Institute of Information Technology, Bangalore.

'''

import math

def fn():
	return

if __name__ == '__main__':
	n, m, k = [int(x) for x in raw_input().split(' ')]
	ls = []
	for times in range(m):
		ls.append(input())
	val = input()
	ans = 0
	for i in ls:
		count = 0
		to_check = bin(i ^ val)
		for j in range(2, len(to_check)):
			if to_check[j] == '1':
				count += 1
		if count <= k:
			ans += 1
	print ans