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:
# You lost the game.
from math import *
n,m,k = map(int, input().split())
L = [int(input()) for _ in range(m+1)]

def binaire(n):
    if n == 0:
        return "0"
    elif n == 1:
        return "1"
    else:
        return str(n%2)+binaire(n//2)

B = [binaire(L[i]) for i in range(m+1)]
B = [B[i]+"0"*(n-len(B[i])) for i in range(m+1)]
R = [0 for _ in range(m)]
for i in range(m):
    for t in range(n):
        R[i] += (B[m][t] != B[i][t])
F = [(R[i]<=k) for i in range(m)]
print(sum(F))