Towers of Hanoi 

In 1883, Edouard Lucas invented, or perhaps reinvented, one of the most popular puzzles of all times - the Tower of Hanoi, as he called it - which is still used today in many computer science textbooks to demonstrate how to write a recursive algorithm or program. First of all, we will make a list of the rules of the puzzle:

• There are three pegs: A, B and C.
• There are n disks. The number n is constant while working the puzzle.
• All disks are different in size.
• The disks are initially stacked on peg A so that they increase in size from the top to the bottom.
• The goal of the puzzle is to transfer the entire tower from the A peg to one of the others pegs.
• One disk at a time can be moved from the top of a stack either to an empty peg or to a peg with a larger disk than itself on the top of its stack.

A good way to get a feeling for the puzzle is to write a program which will show a copy of the puzzle on the screen and let you simulate moving the disks around. The next step could be to write a program for solving the puzzle in a eficient way. You don't have to do neither, but only know the actual situation after a given number of moves by using a determinate algorithm.

The Algorithm

It is well known and rather easy to prove that the minimum number of moves needed to complete the puzzle with n disks is . A simple algorithm which allows us to reach this optimum is as follows: for odd moves, take the smallest disk (number 1) from the peg where it lies to the next one in the circular sequence ; for even moves, make the only possible move not involving disk 1.

Input

The input file will consist of a series of lines. Each line will contain two integers n, m: n, lying within the range [0,100], will denote the number of disks and m, belonging to [0, ], will be the number of the last move. The file will end at a line formed by two zeros.

Output

The output will consist again of a series of lines, one for each line of the input. Each of them will be formed by three integers indicating the number of disks in the pegs A, B and C respectively, when using the algorithm described above.

Sample Input

3 5
64 2
8 45
0 0

Sample Output

1 1 1
62 1 1
4 2 2