You are given a sorted list of n numbers stored in an array A, where n can be arbitrarily large. Now randomly generate a number k and search the number in the list (i.e., in A). Now randomly select two subarrays of A, each of size b [n^1/2]. Then repeat the same procedure on each of the subarrays. The procedure stops after the subarray sizes become 1. Analyze the time complexity of finding the total number of successful searches in the entire procedure using big O-notation.