Problem $2.(18$ points$)$ We have a set of n numbers S$=\{$x$1,$ x$2,$ x$3,...$ xn$\}$ where each number is represented using b bits. We want to partition the elements in Sinto two disjoint sets U and V so that the sum of the elements in U equals the sum of the elements in V$.$ Example $1$ If S$=\{5,1,4,2,6\},$ then U$=\{5,4\}$and V$=\{1,2,6\}.($a$)$ What is the largest possible value forn i$=1$ xi expressed in terms of b and n$?($b$)$ What algorithm that was taught in class does this problem remind you of$?($Give a brief description of the problem and the name to get credit. You can use an example.$)($c$)$ What is the running time for the algorithm from class? Make sure to define whatever parameters you use to describe the running time. $($d$)$ Explain your algorithm for partitioning Sinto Uand V$.$ Use parts $($a$),($b$),$ and $($c$).$