Lexicographically Smallest String After Operations With Constraint

Given a string s and a budget k, find the lexicographically smallest string t you can form by changing characters where each character change costs the cyclic distance on the alphabet and the total cost must be ≤ k. The core challenge is allocating the additive per-character cyclic-change budget to pick the smallest possible letters (often via a greedy per-position decision) while respecting the total cost constraint.