Programs A and B are analyzed and found to have worst$-$case running times no greater than $150($nlogn$)$ and n$2,$ respectively.

Which of the following statements does the analysis imply?

$($a$)$ Program A will run faster on average for sufficiently large n$.$

$($b$)$ Program B will run faster on average for small n$.$

$($c$)$ Program A is probably simpler to code than program B$.$

$($d$)$ There exists some input for which program B takes longer than program A$.$

$($e$)$ none of the above