A $k-$way merge operation. Suppose you have $k$ sorted arrays, each with $n$ elements, and you want to combine them into a single sorted array of $kn$ elements.

$($a$)$ Here's one strategy: Using the merge procedure discussed in the class, merge the first two arrays, then merge in the third, then merge in the fourth, and so on$.$ What is the time complexity of this algorithm, in terms of $k$ and $n?$

$($b$)$ Give a more efficient solution to this problem, using divide$-$and$-$conquer.