The Blah Set

Problem Description

The great mathematician Gauss, as a child, happened upon an interesting set of natural numbers called $Blah$. For a base $a$, the set $Blah$ is defined as follows:

(1) $a$ is the base of $Blah$ and its first element;

(2) if $x$ is in $Blah$, then $2x+1$ and $3x+1$ are also in $Blah$;

(3) there are no other elements.

Little Gauss wants to know: if the elements of $Blah$ are sorted in increasing order, what is the $n$-th element?

Input Format

Two numbers: the base $a$ of the set ($1 \le a \le 50$) and the index $n$ of the requested element ($1 \le n \le 10^6$).

Output Format

The value of the $n$-th element of $Blah$.

Sample Input 1

1 100

Sample Output 1

418

Sample Input 2

28 5437

Sample Output 2

900585

Limitation

1 s, 1024 KiB for each test case.