4. The Index Problem (15 points] Let A be an array of n distinct integers where A is already sorted in ascending order. We would like to find an index i, 1 sis n such that A[i] = i, or prove that no such i exists. (a) Find an O(logn) solution to this problem. (b) Show that any comparison based algorithm for this problem must use 2(logn) compar- isons