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 PYTHON):

Solution:
n,m,k = map(int,raw_input().split())
c = 0
l = []
for i in xrange(m):     l.append(int(raw_input()))

num = bin(int(raw_input()))[2:]

for i in l:
    t = 0
    temp = bin(i)[2:]
    num1 = num
    if len(temp) < len(num1):
        temp = '0'*(len(num1)-len(temp)) + temp
    else:
        num1 = '0'*(len(temp)-len(num1)) + num1
    for j in xrange(len(temp)):
        if temp[j] != num1[j]:  t += 1
    if t <= k:  c += 1
print c