Choose Edges to Maximize Score in a Tree

Given a tree and an integer k, pick k edges whose removal (or selection) maximizes a score defined by each edge's contribution based on the sizes of the two resulting sides when cut (typically subtree_size*(n - subtree_size)). Key ideas are computing subtree sizes to get per-edge contributions, then greedily/strategically selecting and combining the largest contributions (with attention to multiplier handling or modulo arithmetic where required).