$16.(5$ points$)$ Consider the following problems: SUBSET$-$SUM: Given a set of non$-$negative integers a$1,$a$2,...,$an and a target S$,$ does there exist a subset of the integers whose sum is exactly is S$?$ PARTITION: Given a set of non$-$negative integers a$1,$a$2,...,$an$,$ is it possible to partition them into two subsets such that the sum of the elements in both the subsets is equal? Describe a reduction $($informal is OK$)$ showing that PARTITION $$p SUBSET$-$SUM. $[$Hint: Take an instance of PARTITION and produce an instance of SUBSET$-$SUM; or argue why one problem $$captures$$ the other.$]$