One Move from Towers of Hanoi

This problem is about the classic Towers of Hanoi. There are three posts and a collection of circular disks. Call the number of disks $n$. The disks have different sizes, with no two sharing a radius, and there is one rule: never put a bigger disk on top of a smaller one. Number the disks from 1 (smallest) to $n$ (biggest) and name the posts A, B, and C. All the disks start on post A, and the goal is to move them to post C one at a time, again never putting a bigger one on top of a smaller one. The well-known solution recursively moves the top $n-1$ disks from A to B, moves the bottom disk from A to C directly, then recursively moves those $n-1$ disks from B to C.

Pseudocode for a recursive solution to the classic Towers of Hanoi problem:

move(num_disks, from_post, spare_post, to_post)
    if (num_disks == 0)
        return
    move(num_disks - 1, from_post, to_post, spare_post)
    print ("Move disk ", num_disks, " from ",
        from_post, " to ", to_post)
    move(num_disks - 1, spare_post, from_post, to_post)

Given $k$ and $n$, determine the $k$th move made by the algorithm above.

Each line of input holds two integers $k$ and $n$. A line with two zeros marks the end of input.

All input is valid. $k$ and $n$ are positive integers, $k < 2^n$ so that a $k$th move exists, and $n \le 60$ so that the answer fits in a 64-bit integer type.

For each test case, print the $k$th move made by the algorithm above. Follow this format exactly: Case, one space, the case number, a colon and one space, then the answer for that case given as the number of the disk, the name of the from_post, and the name of the to_post, with one space separating the parts of the answer. Do not print any trailing spaces.