Xiao C opened a hotel called CC Hotel.

One day, $n$ guests arrived at CC Hotel. Xiao C needs to accommodate all of them on a single floor of the hotel. Each room can accommodate only one guest.

There are $m$ rooms on this floor, all of which are currently empty. These $m$ rooms are arranged in a circle, meaning that for all $1 \le x \le m$, room $x$ is adjacent to room $((x \bmod m)+1)$, and room $((x \bmod m)+1)$ is adjacent to room $x$, where $x \bmod m$ denotes the remainder of $x$ divided by $m$.

The $n$ guests are very picky; they wish for no one to be in the rooms adjacent to their own. For a given guest, if $k$ rooms adjacent to their room are occupied, this guest will generate $k$ points of anger.

You need to help Xiao C arrange the rooms to minimize the total sum of anger values of all guests, and output this minimum sum.

Input

Two integers $n, m$.

Output

A single integer representing the minimum total sum of anger values of all guests.

Examples

Input 1

3 5

Output 1

2

Note 1

For these $5$ rooms, one possible arrangement satisfying the conditions is: empty, occupied, occupied, empty, occupied.

It can be proven that the minimum total sum of anger values for all guests is $2$.

Input 2

1 4

Output 2

0

Constraints

For $100\%$ of the data, $1 \le n \le 100$, $3 \le m \le 100$, and it is guaranteed that $n \le m$.