i dont read the editorial but my solution was that if in the tree a node like v has sz[v] nodes in its subtree if(sz[v] < a[v]) its impossible to reach the goal. else you can give the weights of its subtree nodes a permutation then for a new vertex you can merge its children permutation to make bigger permutation and then for the root you can actully give the nodes the last permutation if you want you can see my soloution in my submissions