"Given a balanced binary tree, describe a procedure to perform all-to-all broadcast that takes time (ts + tw * mp/2) * log(p) for m-word messages on p nodes. Assume that only the leaves of the tree contain nodes, and that an exchange of two m-word messages between any two nodes connected by bidirectional channels takes time ts + tw * mk if the communication channel (or part of it) is shared by k simultaneous messages."