Problem Statement

When you woke up in the morning, there was a mysterious electronic device in front of you. This device can display integers from $1$ to $N$, and it initially displays $1$.
It also has two buttons: pressing the first button increases the displayed number by $1$, and pressing the second button decreases it by $1$.
However, if the first button is pressed while $N$ is displayed, the next number displayed is $1$, and if the second button is pressed while $1$ is displayed, the next number displayed is $N$.
How many different numbers could be displayed after pressing the $2$ buttons exactly $K$ times in total?

Input

$N\ K$

$1 \le N \le 10^9$
$1 \le K \le 10^9$
$N, K$ are integers.

Output

Output the answer, followed by a newline.

Sample

3 1

2

6 3

3

5 3

4