B$-$trees: $10$ points $($please show the work $/$ steps for the following$)$:

Construct a B$-$tree with $t=3$ using the following sequence of operations

$[5$ pts$]$ Insert the following numbers in the order as they are given:

$1,11,2,23,8,13,27,5,18,29,7,4,44,21,2,52,9,31,15,46,15,12,43,17$

$[5$ pts$]$ Delete $8,$ and then delete $52$

Skip Pointers: $5$ points

For the posting list pointers p$1$ and p$2($initially pointing at docIDs $2$ and $1),$

show how the values pointed at by the pair $($ p $1$ and p $2)$ changes at each step of

the intersection using skip pointers $($as defined in the algorithm below$).$