A disk page $($B$)$ contains $512$ bytes. The search key $($K$),$ data

record $($R$),$ and page id $($P$)$ use $8$ bytes, $64$ bytes and $4$ bytes, respectively. Data entries use

Alternative $(1),$ i$.$e$.,$ pair $.$ A leaf node has a $$previous$-$leaf pointer$$ and a $$next$-$leaf$-$pointer$.$

That is$,$

a$.$ Compute the order of the B$+-$tree. The order for leave nodes and index nodes may be

different.

b$.$ Given the above parameters, what is the minimum number of data records that a $2-$level

B$+-$tree $($not counting the root$)$ can index.

c$.$ Given the above parameters, what is the minimum number of levels required of a B$+-$tree to

index $100,000$ records