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## ACM_0102 - ONE MOVE FROM TOWERS OF HANOI

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 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 1 (smallest) to n (biggest) and name the posts A, B, and C. If all the disks start on post A, and the goal is to move the disks to post 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 n–1 disks from A to B, then directly moves the bottom disk from A to C, then recursively calls for moving the n–1 disks from B to C.

Pseudocode for a recursive solution to 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)

The problem at hand is determining the kth move made by the above algorithm for a given k and n.

#### Input

Input will be two integers per line, k and n. End of file will be signified by a line with two zeros. All input will be valid, k and n will be positive integers with k less than 2n so that there is a kth move, and n will be at most 60 so that the answer will fit in a 64-bit integer type.

#### Output

Output the requested kth move made by the above algorithm. Follow this format exactly: “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 from_post, and the name of the to_post with one space separating the parts of the answer. Do not print any trailing spaces.

#### Examples

 № stdin stdout 1 1 3 5 3 8 4 0 0 Case 1: 1 A C Case 2: 1 B A Case 3: 4 A C

 Ավելացրեց. Հրանտ Հովհաննիսյան Ամսաթիվ. 2014-01-28 Ժամանակի սահմանափակումը. 1s Ծրագրի տեքստի սահմանափակումը. 50000B Memory limit: 1536MB Cluster: Cube (Intel G860) Լեզուներ. Բոլորը բացի ASM32 ASM64 GAWK CLPS CLOJURE D ERL FSHARP FORTRAN GOSU HASK ICON ICK NEM NIM OBJC-CLANG PICO PIKE PYPY PY_NBC RUST SCM guile CHICKEN SED TCL WHITESPACE Աղբյուրը. NA North Central 2013.C