Question B $[20$ points$]$

Consider the following $B+$ tree with order $d=5$ and height $h=2.$

When answering the following questions, please follow the assumptions:

A left pointer in an internal node guides towards keys smaller than its corresponding key, while a right pointer guides towards keys larger or equal than its corresponding key.

A leaf or internal node underflows when the number of pointers goes below $2.$

$1.$Insert $41$ into the $B+$ tree. Draw the resulting tree. $[10$ marks$]$

$2.$Delete $120$ from the original B$+$ tree. Draw the resulting tree. $[10$ marks$]$