In any search algorithm, if a given sequence A is sorted, we can check the midpoint v of A against the rest of the elements in A and eliminate the half of the sequence from the further consideration. The binary search algorithm repeats this procedure, halving the size of the remaining portion of the sequence each time. Write pseudocode for a recursive binary search algorithm for a given sequence A and a key value x to find. Argue that the worst-case running time of binary search is theta(log n)