(a) Let S,NEN. Using the notation we've used in class, write a simple loop for computing SN. (Do not assume you can use an exponentiation operator, the "=" operator, and a while loop. Create whatever variables you need.) Use only (b) Provide a loop invariant, p, for your code, and prove its correctness by showing that p^ B{S}p is a good Hoare triple. (p ^ B){S}p p{while B do S}(p^-B) Use the "While loop inference rule above, and the fact that p is a good loop invariant, to prove that your code outputs SN