Minimum Changes to Make K Semi-palindromes

Partition the string s into k contiguous substrings to minimize the total number of character changes, where the cost of a substring is the minimum edits needed to make it a semi-palindrome — i.e., for some divisor d of the substring length, each of the d periodic groups (positions congruent mod d) forms a palindrome. Return the minimum possible sum of those per-substring costs.