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:
w=input().split(" ")
n=int(w[0])
m=int(w[1])
k=int(w[2])
arr=[]
for i in range(m+1):
	arr.append(int(input()))
f=0
ar=[]
for i in range(m+1):
	p=n
	type=""
	while p>-1:
		q=arr[i]//(2**p)
		type=type+str(q)
		arr[i]=arr[i]-(q*(2**p))
		p=p-1
	ar.append(type)
for i in range(m):
	ck=0
	for j in range(len(ar[0])):
		if ar[i][j]==ar[m][j]:
			ck=ck+1
	if abs(ck-(n+1))<k+1:
		f=f+1
print(f)