For this problem consider the problem of finding the sum of a list of integers. Sum of All Integers in a List (SUM) Input: A list of integers A[a...b]. Output: s = sigma^b _i = a A[i]. Let S(A[a...b]) represent the output of the SUM problem on input A[a...b]. State two different self-reductions for the SUM problem. Use the self-reduction examples from lecture as a guide. Give recursive algorithms based on your divide and conquer self-reductions to solve the SUM problem. What are the worst case runtimes of the solutions you have generated. (Just state the runtimes. You do not need to show your work.)