Petya is a rifleman. He is located in the leftmost bottom cell of the rectangular field Nx M, all other cells of the field are occupied by enemies. Petya and his enemies are points and they are located in the centers of the corresponding cells. Petya has a power supersecret weapon Ber-9875 which destroys all enemies along a straight line. Your task is to calculate the minimum number of shots to do this.

The first line of the input contains two integers N and M (1≤ N, M≤ 10⁶).

Output file must contain the minimum number of shots.

sample input	sample output
3 4	7

sample input	sample output
2 10	11