Let T be a binary tree with n nodes, and let p be the level numbering of the nodes of T, so that the root, r, is numbered as p(r)=1, and a node v has left child numbered 2p(v) and right child numbered 2p(v)+1, if they exist. 

a. Show that, for every node v of T, p(v) ≤ 2^(n+1)/2 − 1. 

b. Show an example of a binary tree with at least five nodes that attains the above upper bound on the maximum value of p(v) for some node v.