def generate_k_type_1(n)
    k = Array.new
    divisor = 2
    new_k = n

    while new_k != 1
      new_k = (n / divisor).floor

      divisor *= 2
      k.push(new_k)
    end

    k
  end

  def generate_k_type_2(n)
    k = Array.new
    power = 1
    max = n / 3

    while true
      new_k = (3 ** power - 1) / 2
      power += 1

      if new_k <= max
        k.push(new_k)
        next
      end

      break
    end

    k.reverse
  end

  def generate_k_type_3(n)
    k = Array.new
    max_r = Math.log(n, 2).floor
    max_s = Math.log(n, 3).floor

    for r in 0..max_r
      for s in 0..max_s
        new_k = (2 ** r) * (3 ** s)

        if new_k < n
          k.push(new_k)
        end
      end
    end

    k.sort.reverse
  end