There are multiples parts to this question. Be sure to clearly indicate your answer for each part. Consider this program and its specification. # Pre: n, p, s are integers; 2 < p < n; p is a prime number; In mod p != 0; 0 n: if x < 0: 0: 6. if m == 7. else: * m = s mod p * -1 d; -1 * d; return 'happy' d = d = return 'sad' X = n - (x - n); m = x mod p X = -1 * X; m = X Part (a): Briefly explain why the loop iterates fewer than 2n times if it terminates. A rigorous proof is not expected. You just need to show appropriate insight. Part (b): Give an appropriate loop invariant for proving that Bounce is partially correct. Be careful here. Your answer to part (c) relies on a correct answer to part (b). Part (c): Use your loop invariant from part (b) to prove that Bounce is partially correct.