Please explain CENTREE in cook83

CENTREE in COOK83: Can somebody explain what to do in the question? Or upload the editorial please

My approach was to make a linked list graph of size at most \lfloor \frac{n}{2} \rfloor + 1. The midpoint will be the center. To make a centroid, stick remaining nodes one-by-one to the node located at midpoint + b of the linked list. Take care of special cases for small n, then we can have a tree with beauty of b.

Link to solution