Matcom Online Grader
Faculty of Mathematics and Computer Science of University of Havana

The most difficult problem that players must face during a LAN isn’t precisely defeat each other on DOTA or COD. The real problem arises when the game ends and some player must stay out the next game. No one wants to go out, that why the LAN party of our boy invented the following algorithm to decide who goes out each round. At the end of each game all $N$ players form a row, each player gets a number between $1$ and $N$. Some random number $M$ is generated using their computers. Then each player from $1$ to $N$ get a number between $1$ and $M$, this is: player with number $1$ gets $1$, players with number $M$ gets $M$, player with number $M + 1$ gets $1$ again and so on until players $N$ gets its number. When this first step is made all players with number $1$ assigned can safely go to their computers and be ready for the next game, the rest form a new row possibly using the space left by their friends. The procedure last until a single player left. This poor guy must leave the next game. Our boy knows that despite the amount of calculations needed, the loosing position can be known before the algorithm starts so he ask you to quickly calculate it giving to him the chance to avoid it.

Input

Two integers $N$ $(2 \leq N \leq 10^6)$, $M$ $(2 \leq M \leq N)$, the number of players and a random number $M$.

Output

The loosing position.

Sample test(s)

Hints

First Case

1 2 3 4 5
1 2 3 1 2
2 3 5
1 2 3
3 5
1 2
5