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:
def countOnes(string):
	cnt = 0
	for i in string:
		if i == '1':
			cnt+=1
	return cnt



l = [int(i) for i in raw_input().split()]

n = l[0]
m = l[1]
k = l[2]

l1 = []
for i in range(m):
	inp = int(raw_input())
	l1.append(inp)
#	l.append(bin(inp))

inp1 = int(raw_input())
cnt = 0
#k = bin(inp1)
for j in l1:
	if countOnes(bin(inp1^j)[2:]) <= k:
		cnt +=1
#l2 = [(inp1,j) for j in l1 if countOnes(bin(inp1^j))[2:] <= k]
print cnt
#print len(l2)