$[20\%]$ Consider the following B$+-$tree. Insert the keys $1,17,89,42,74$

in it in order. Show the tree after each insertion operation.

If a non$-$leaf node contains $x$ pointers and splitting is needed,

distribute the floor$($x$/2)$ pointers to the node on left and roof$($x$/2)$

pointers to the node on right.

$[20\%]$ Consider the following B$+-$tree. Delete the keys $99,82,73,69$ from it in order. Show the tree after each deletion operation.

Assume that if merging or redistribution of a node is necessary, it's left sibling, if exists, is used first.