(a) Construct a B+ tree (initially empty) for the following set of key values (in this order): (insert 2, insert 3, insert 5, insert 7, insert 11, insert 17, insert 19, insert 23, insert 29, insert 31, insert 9, insert10, insert 8, delete 23, delete 19). Assuming order (i.e., the number of pointers that will fit in one node) is 4. Also assuming max number of key values each leaf node is same as the max number of key values of internal nodes. Show steps of your work. Include a new figure each time when the shape of the B+ tree is changed; i.e., when each time a node is split or two nodes are combined, a new figure including all elements so far have been inserted into the tree should be drawn.

(b) Redo part (A) with order = 6. Show steps.

(c) Comparing (a) and (b). What is your observation on the impact of the B+ tree order (i.e., the value of m) to B+ tree operations? In particular, when m gets bigger, what are the pros and cons? Overall, will you prefer larger or smaller values of m?