During his excursion to the historical park, Pepito set out to collect stones whose weight in kilograms is a power of two. Once the first stone has been collected, Pepito only collects stones strictly heavier than the first. At the end of the excursion, her partner Ana chooses a positive integer $K \ge 2$ and challenges Pepito to divide the stones into $K$ groups of equal weight. a) Can Pepito meet the challenge if all the stones he collected have different weights? b) Can Pepito meet the challenge if some collected stones are allowed to have equal weight?