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:
while True:
	try:
		def count_one(num):
			s = 0
			while num != 0:
				s += num%2
				num //= 2
			return s
			
		def solution(n, m, k, fedr, a):
			frnd = 0
			for i in range(m):
				num = a[i] ^ fedr
				num = count_one(num)
				if num <= k:frnd += 1
			print(frnd)
			
		def read():
			n, m, k = map(int, input().split())
			a = []
			fedr = 0
			for i in range(m):
				a.append(int(input()))
			fedr = int(input())
			solution(n, m, k, fedr, a)
			
		if __name__ == "__main__":
			read()
	except EOFError:
		break