Problem Statement

There is a stack of cards with the numbers from $1$ to $N$ written on them, piled in numerical order so that $1$ is on top and $N$ is on the bottom. This state is called the initial state.

These cards are to be shuffled, and there are the following 2 kinds of shuffles.
Swap shuffle: swap two vertically adjacent cards
Magician shuffle: take the top card and insert it somewhere between the other cards

For example, when the cards are $3, 4, 2, 1$ from the top, a swap shuffle can produce any one of the states $4, 3, 2, 1$ and $3, 2, 4, 1$ and $3, 4, 1, 2$, and a magician shuffle can produce any one of the states $4, 3, 2, 1$ and $4, 2, 3, 1$ and $4, 2, 1, 3$.

Starting from the initial state, eiram performed a magician shuffle that inserted the top card between the cards with $K$ and $K + 1$ written on them.
nauclhlt likes going against the crowd, so he decided to try reproducing the same state from the initial state using only swap shuffles. What is the minimum number of swap shuffles required?

Input

$N\ K$

$3 \le N \le 10^{10}$
$2 \le K \lt N$

Output

$ans$

Sample

5 3

2