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:
# Code Author : Jayesh Udhani
# College	  : DA-IICT
# This is my 5th code in python

def solver(x,y,z):
   k=0
   t=min(len(x),len(y))
   for i in range(t):
   	if x[i]!=y[i]:
   		k+=1
   if len(x)<len(y):
   	for i in range(len(x),len(y),1):
   		if y[i]=='1':
   			k+=1
   elif len(y)<len(x):
   	for i in range(len(y),len(x),1):
   		if x[i]=='1':
   			k+=1
   return k<=z;
a=list(input().split(" "))
l=[]
c=0
for i in range(int(a[1])+1):
	l.append((bin(int(input()))[2:])[::-1])
for i in range(int(a[1])-1,-1,-1):
	if solver(l[int(a[1])],l[i],int(a[2])):
		c+=1
print(c)