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:
l1=[int(x) for x in input().split()]#n,m,k.
m=l1[1]
l2=[]
fri=0
for i in range(0,m+1):
	l2.append(int(input()))
check=list(str(bin(l2[m])))
check.pop(0)
check.pop(0)
for j in range(0,m):
	count=0
	checkdash=list(str(bin(l2[j])))
	checkdash.pop(0)
	checkdash.pop(0)
	for k in range(0,abs(len(checkdash)-len(check))):
		if(len(checkdash)>len(check)):
			check.insert(0,'0')
		else:
		    checkdash.insert(0,'0')
	maxi=max(len(checkdash),len(check))
	for	l in range(0,maxi):
		if(checkdash[l]!=check[l]):
			count+=1
	if(count<=l1[2]):
	    fri+=1
print(fri)