Professor Bunyan asserts that the insertion procedure of a 2-3-4 tree (or B-Tree-Insert for t = 2) always results in a tree with minimum possible height. Show the professor is mistaken by

(a) Draw the tree that results from inserting, into an empty tree, the values 1, 2, 3, ..., 15 in that order.

(b) Draw a 2-3-4 tree of minimum height with the keys {1, 2, ..., 15}.