Consider the following "PARTITION" search problem. input. A set of integers S = {xi, X2, , Xal_ each integer can be positive, negative, or zero. Output: A partition of S into subsets S1,S2 with equal sum, if such a partition is possible; otherwise return the special value NIL. (S1.S2 is a "partition" of S if every element of S belongs to one of S1 or S2, but not to both.) (a) [5 marks] Give a precise definition for a decision problem "PART" related to the PARTITION search problem. (b) [15 marks] Give a detailed argument to show that the PARTITION search problem is polynomial- time self-reducible. (WARNING: Remember that the input to the decision problem does not contain any information about the partition-if it even exists.)