Dinner Plate Stacks

Implement a data structure of infinite fixed-capacity stacks that supports push to the leftmost stack with available space, pop from the rightmost non-empty stack, and popAtStack(index) removing the top of a specific stack. The algorithmic challenge is to efficiently track which stacks are non-full and non-empty (e.g., with heaps/ordered sets) to handle up to 2e5 operations.