You are given a array $A$[0..$n$-1]$$ containing n comparable keys. We would like to determine the smallest, third smallest, fifth smallest, and seventh smallest of the n keys. Moreover we would like to determine the largest, third largest, fifth largest and seventh largest of the n keys. Design an algorithm to do so$,$ count carefully and compute a tight upper bound on the number of comparisons performed and state the constants a and b of that bound. A desirable comparison bound count is of the form$$

K$*$ n $*$ lgn $+$ L$*$n $+$ o$($n$)$ where K is as small $($and thus close to zero as possible$)$ and b as small as possible and smaller than $8.$

$($a$)$ Provide$$ the value of K $=$

$($b$)$ Provide the value of$$ L$=$

$$