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:
import sys
def input():
    return sys.stdin.readline().strip()
 
 
def iinput():
    return int(input())
 
 
def tinput():
    return input().split()
 
 
def rinput():
    return map(int, tinput())
 
 
def rlinput():
    return list(rinput())

n,m,k = rinput()
A = [0]*(m+1)
for i in range(m+1):
    A[i] = iinput()
target = bin(A[m])[2:]
ans = 0
for i in range(m):
    current = bin(A[i])[2:]
    if len(target) < len(current):
        target = '0'*(len(current)-len(target)) + target
    else:
        current = '0'*(len(target)-len(current)) + current
    error = 0
    flag = True
    for i in range(len(target)):
        if target[i] != current[i]:
            error += 1
            if error > k:
                flag = False
                break
    if flag:
        ans += 1
print(ans)