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 math
n, m, k = map(int, (input().split()))
mm = m
nn = n
bin = []
while m+1:
    m -= 1
    num = int(input())
    temps = ''
    while math.floor(num) != 0:
        r = num % 2
        temps += str(r)
        tempd = n-len(temps)
        num = math.floor(num/2)
    tempd = nn-len(temps)
    temps += '0'*tempd
    bin.append(temps)
fedor = bin[-1]
c = mm
for i in bin:
    comp = i
    diff = 0
    z = 0
    while z < nn:
        if fedor[z] != comp[z]:
            diff += 1
        z += 1
    if diff > k:
        c -= 1
print(c)