Longest Palindromic Subsequence After at Most K Operations

Given a string s and a budget k of single-step cyclic letter shifts (each operation moves a character to its next or previous letter, wrapping a↔z), find the maximum length of a palindromic subsequence you can obtain with at most k operations. Core challenge: dynamic programming over pairs to maximize palindrome length under a global cost constraint where the cost to match two chars is their minimal cyclic distance.