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 $6 \to 3 \to 10 \to 5 \to 16 \to 8 \to 4 \to 2 \to 1$.

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 $n \le 4035225266123964416$.

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

    void converge(int n, int& k, int& far);

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 $1 \le m \le 50000$.

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.