6. BONUS Challenge Question (not required to be submitted but bonus marks will be awarded for correct solu tions). Given a sorted array A[L of infinite length, and a real number r, the goal is to find an index i such that Alil 2 r. Let m be the first index in A such that Afm] 2 . (a) (1 pt) Give an algorithm that finds an index i in O(log m) time. Prove the correctness and runtime of your algorithm. (b) (2 pts) Give an algorithm that finds an index i in O(log log m) time. Prove the correctness and runtime of your algorithm