Problem
Given an array A[1 . . . n] whose elements are odd numbers (positive and negative). Suppose that n is a power of 2, the elements in A[1 . . . n] are sorted and distinct. Design an algorithm to check whether there is at least one element in the array satisfies A[i] = 2i + 5, where 1 ≤ i ≤ n is the index of the ith element in the array. If such element exists, your algorithm should return "yes"; otherwise, return "no". The running time of your algorithm is required to be O(log(n)). Describe your algorithm with words (no pseudocode) and explain why it is correct. Justify the running time of your algorithm.