$$ Reserves $($R$)$: $100,000$ tuples stored in $1,000$ pages. There are $100$ boats. Each boat is equally poplar $($i$.$e$.,$ each has the same number of reservations$).$ Sailors $($S$)$: Stored in $500$ pages. There are $10$ distinct rating levels $(1$ to $10),$ each with the same number of sailors.$1.$ The sid column takes up $25\%$ of the data size of the Reserves relation. The sid and sname columns take up $75\%$ of the data size of the Sailor relation.$$a$.$ If you are given $3$ memory pages, describe an efficient execution plan for the execution tree in the right.$$b$.$ Estimate the processing time $($in terms of I$/$O cost$)$ of your computation strategy. You do not have to include the cost of writing the query result in your analysis.