Subtree Inversion Sum

Choose a set of nodes whose subtree values are negated to maximize the total sum, with the constraint that any two inverted nodes that are ancestor and descendant must be at least k edges apart. This is a rooted-tree selection problem with long-range ancestor–descendant constraints (n up to 5e4, k ≤ 50), typically solved by a tree DP tracking distances/parities of flips along paths.