Lexicographically Smallest Beautiful String

Given a beautiful string s over the first k lowercase letters, find the lexicographically smallest string of the same length that is strictly greater than s and contains no palindromic substring of length ≥2 (i.e., forbids equal adjacent letters and patterns like a_b_a). This is essentially the "next lexicographic string under local no-palindrome constraints" problem, solvable by greedy increment with backtracking.