1. (10 marks) You decided to modify mergesort by recursively splitting an array of size n into k sorted subarrays; k > 2, and merging these subarrays. Time for merging is c(k-1)n where c is a constant factor, because at each step the largest item among the k top ones in the k subarrays is found by k - 1 comparisons and placed into the merged array. Specify the recurrence relation and derive the closed-form formula for sorting time Tk(n) of the modified mergesort for an arbitrary k (you should show all steps of the derivation) Then determine whether the modified mergesort could be faster for some k > 2 than the conventional one (k = 2) with the sorting time T2 (n) = cn log2 n. Hint: To have a well-defined recurrence, assume that n - km with the integer m - logk n and T(1)- 0. You might need also the equality log2 -log2k logk r for all r > 0 and the inequality k > 1 log2 k for all k > 2