human
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
The above is tricky. Write me a correct solution in PYTHON3.
assistant
#Here is Python code to print a single integer — the number of Fedor's potential friends.

# def checkKey(dict, key): 
# 	if key in dict:
# 		return True
# 	return False
# def helper(s):
# 	l=len(s)
# 	if (l==1):
# 		l=[]
# 		l.append(s)
# 		return l
# 	ch=s[0]
# 	recresult=helper(s[1:])
# 	myresult=[]
# 	myresult.append(ch)
# 	for st in recresult:
# 		myresult.append(st)
# 		ts=ch+st
# 		myresult.append(ts)

# 	return myresult

# mod=1000000000+7
# def helper(s,n,open,close,i):
# 	if(i==2*n):
# 		for i in s:
# 			print(i,end='')
# 		print()
# 		return
# 	if(open<n):
# 		s[i]='('
# 		helper(s,n,open+1,close,i+1)
# 	if(close<open):
# 		s[i]=')'
# 		helper(s,n,open,close+1,i+1)

# def helper(arr,i,n):
# 	if(i==n-1):
# 		recresult=[arr[i]]
# 		return recresult
# 	digit=arr[i]
# 	recresult=helper(arr,i+1,n)
# 	myresult=[]
# 	for i in recresult:
# 		myresult.append(i)
# 		myresult.append(i+digit);
# 	myresult.append(digit)
# 	return myresult
# import copy
# n=int(input())
# arr=list(map(int,input().split()))
# ans=[]
# def helper(arr,i,n):
# 	if(i==n-1):
# 		# for a in arr:
# 		# 	print(a,end=" ")
# 		# print()
# 		l=copy.deepcopy(arr)
# 		ans.append(l)
# 		return
# 	for j in range(i,n):
# 		if(i!=j):
# 			if(arr[i]==arr[j]):
# 				continue
# 			else:
# 				arr[i],arr[j]=arr[j],arr[i]
# 				helper(arr,i+1,n)
# 				arr[j],arr[i]=arr[i],arr[j]
# 		else:
# 			arr[i],arr[j]=arr[j],arr[i]
# 			helper(arr,i+1,n)
# 			arr[i],arr[j]=arr[j],arr[i]
def set_bits(n,k):
	c=0
	while(n>0):
		n=n&(n-1)
		c+=1
	if(c<=k):
		return True
	return False

n,m,k=map(int,input().split())
l=[]
for i in range(m):
	l.append(int(input()))
fedor_army=int(input())
ans=0
for i in l:
	temp=fedor_army^i
	if(set_bits(temp,k)):
 		ans+=1
print(ans)