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:
def binary(number):
	li=[]
	while (number!=0):	
		z=number%2
		li.append(z)
		number=int((number-z)/2)
	if number==0:
		li.append(0)
	return li	
g=input()
n,m,k=[int(x) for x in g.split()]
gamers={}
for i in range(1,m+2):
	f=int(input())
	gamers[i]=binary(f)
listing=gamers[m+1]
fedor=len(listing)	
count=0
for j in range(1,m+1):
	l=0
	t=0
	faltu=gamers[j]
	fa=len(faltu)
	for itr in range(min(len(listing),len(faltu))):
		if faltu[itr]!=listing[itr]:
			l=l+1	
		if l>k:
			t=1
			break				
	if fedor>fa:
		for it in listing[(fa):]:
			if it==1:
				l=l+1
			if l>k:
				t=1
				break	
	if fedor<fa:
		for itt in faltu[(fedor):]:
			if itt==1:
				l=l+1
			if l>k:
				t=1
				break	
	if t==0:
		count+=1
print(count)