For this problem, we are concerned with the classic problem of Towers of Hanoi. In this problem there are three posts and a collection of circular disks. Let’s call the number of disks \textbf{n}. The disks are of different sizes, with no two having the same radius, and the one main rule is to never put a bigger disk on top of a smaller one. We will number the disks from \textbf{1} (smallest) to \textbf{n} (biggest) and name the posts \textbf{A}, \textbf{B}, and \textbf{C}. If all the disks start on post \textbf{A}, and the goal is to move the disks to post \textbf{C} by moving one at a time, again, never putting a bigger one on top of a smaller one, there is a well-known solution that recursively calls for moving \textbf{n--1} disks from \textbf{A} to \textbf{B}, then directly moves the bottom disk from \textbf{A} to \textbf{C}, then recursively calls for moving the \textbf{n--1} disks from \textbf{B} to \textbf{C}. Pseudocode for a recursive solution to classic Towers of Hanoi problem: \textbf{move(num_disks, from_post, spare_post, to_post)} \textbf{if (num_disks == 0)} \textbf{return} \textbf{move(num_disks -- 1, from_post, to_post, spare_post)} \textbf{print ("Move disk ", num_disks, " from ", from_post, " to ", to_post)} \textbf{move(num_disks -- 1, spare_post, from_post, to_post)} The problem at hand is determining the \textbf{k}^th move made by the above algorithm for a given \textbf{k} and \textbf{n}. \InputFile Input will be two integers per line, \textbf{k} and \textbf{n}. End of file will be signified by a line with two zeros. All input will be valid, \textbf{k }and \textbf{n} will be positive integers with \textbf{k} less than \textbf{2^n} so that there is a \textbf{k}^th move, and \textbf{n} will be at most \textbf{60} so that the answer will fit in a \textbf{64}-bit integer type. \OutputFile Output the requested \textbf{k}^th move made by the above algorithm. Follow this format exactly: "\textbf{Case}", one space, the case number, a colon and one space, and the answer for that case given as the number of the disk, the name of the \textbf{from_post}, and the name of the \textbf{to_post} with one space separating the parts of the answer. Do not print any trailing spaces.