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:
def differing_bits(a_army, b_army, n):
    count = 0
    for i in xrange(n):
        if (a_army & (1 << i) != 0 and b_army & (1 << i) == 0) or (a_army & (1 << i) == 0 and b_army & (1 << i) != 0):
            count += 1
    return count


[n, m, k] = map(int, raw_input('').split(' '))
armies = [0] * m
for i in xrange(m):
    [army] = map(int, raw_input('').split(' '))
    armies[i] = army
[fedor_army] = map(int, raw_input('').split(' '))
count = 0
for army in armies:
    if differing_bits(fedor_army, army, n) <= k:
        count += 1
print count