You are given a sorted array S[1, . . . , n] of n (distinct) numbers, i.e., the numbers in the array are arranged in increasing order: S[1] < S[2] < < S[n]. Give a recursive algorithm to search for a given element (say x) in the array. If x is present in the array, the algorithm should return the index of the position where it is present, otherwise it should return 0. Your algorithm should take O(log n) comparisons. Give pseudocode of your algorithm and argue that your algorithm indeed takes O(log n) comparisons (in the worst case).