$($a$)$ Suppose you want to implement the merge operation from MergeSort, but instead of merging $2$ arrays, you want to merge k arrays, each of length n$.$ One way to do this is by first merging the first array and the second ar$-$ ray, and then merging the result with the third array, and then merging the result with the fourth array, etc. What is the running time of the described algorithm? $($b$)$ Present a more efficient divide$-$and$-$conquer solution to this problem. What is its running time?