Bookshelf

Doctor Strange keeps a large library in his mansion. Today he is thinking about the domino effect, and books help with that even if nobody reads them.

The Sorcerer Supreme has an infinite number of ultra-thin books of height $h$. The bookshelf can be viewed as a number line, and books can only be placed at integer coordinates. Wong has already placed books at coordinates $0$ and $r$.

A book at coordinate $a$ knocks over a book at coordinate $b$ when it falls, if at the moment the top point of the first book is at coordinate $b$ and height $y$, then $y \ge \frac{h}{2}$. The thickness of a book is negligible.

Strange had to work through $14\,000\,605$ possible futures to find the minimum number of books that must be placed between the two original ones, so that pushing the book at coordinate $0$ can eventually topple the book at coordinate $r$. Wong does not know this kind of magic, so he asks you to solve this puzzle.

The first line contains one even positive integer $h$, the height of the books ($2 \le h \le 10^6$).

The second line contains one positive integer $r$, the coordinate of the rightmost book ($1 \le r \le 10^6$).

Print one number: the minimum number of books that must be placed so that pushing the leftmost book can topple the rightmost book.