$(24$ points$)$ Using the following B$+$ Tree index, answer the questions that follow: $($show all work$)$

Every node can contain $m$ entries, where $2m4$

The root node is an exception: it allows $1m4$

I. Show the resulting $B+$ Tree after deleting data entry $42**$

II$.$ Using the tree derived from part $($I$)$ above, show the resulting B$+$Tree after inserting data entry $7*$

III. Using the tree derived from part $($II$)$ above, show the resulting B$+$Tree after inserting data entry $31**$

Draw separate B$+$ tree for I, II$,$ and III and describe the steps $($Show all work$)$