P0017. Siracusa attacks again P14410

Being n a natural number greater than zero. Consider this algorithm:

• If n = 1, stop.
• If n is an even number, divide it by 2.
• If n is an odd number, multiply it by 3 and add 1.

For instance, starting with 6 we obtain 6 → 3 → 10 → 5 → 16 → 8 → 4 → 2 → 1.

The conjecture 3n + 1 says that starting with any natural number n > 0, it always arrives to 1. Although it has not still been proved, using computers we know that is true for numbers n ≤ 4035225266123964416.

Your task is to write a program that reads two natural numbers m and p and prints which natural numbers between 1 and m arrive to 1 in p or more steps. It must print also which is the greatest number contained in their steps.

Your program must implement and use the procedure

that, given an integer strictly positive |n|, stores at the parameter |k| the number of steps that needs |n| to arrive to 1, and at the parameter |far| the greatest number seen in the process. For instance, |converge(6, k, far);| stores an 8 at |k| and a 16 at |far|. Similarly, |converge(4, k, far);| stores a 2 at |k| and a 4 at |far|, and |converge(1, k, far);| stores a 0 at |k| and an 1 at |far|.

Input

The input is two natural numbers m and p, with 1 ≤ m ≤ 50000.

Output

Your program must print all the numbers between 1 and m that arrive to 1 in p or more steps, one per line. Besides, print also the greatest produced number, following the format of the instances.