Consider the B$+$ tree index.

Every node can contain m entries, where m

The root node is an exception: it allows m

B$+$ tree

A$.$ Show the B$+$ tree that would result from inserting data entries with key $30,33,$ and $41$ into the tree.

$($Insert each entry one at a time and show all work$)($Please don't do one B$+$ tree with results A$,$ B$,$ C$,$ and D$)$

B$.$ Given the output of $($A$),$ show the B$+$ tree that would result from deleting the data entry with key $3.$

C$.$ Given the output of $($B$),$ show the B$+$ tree that would result from deleting the data entry with key $4.$

D$.$ Given the output of $($C$),$ show the B$+$ tree that would result from deleting the data entry with key $15.$