Find the Lexicographically Largest String From the Box II

Given a string of letters and a limited set of operations that move letters from the "box" to an output (with the ability to defer and reorder under constraints), construct the lexicographically largest output string possible. The core challenge is designing a greedy/stack-based strategy that decides when to emit a character versus postpone it, using remaining-frequency or next-max information to ensure global optimality.