Billiards is a rectangle with the sizes of
N is natural numbers. From an overhead left pocket a bullet takes off under the corner of 45° to the nearby sides. The pockets are placed only in the corners of billiards. You have to define the quantity of collisions of bullet with the sides of billiards, after which it again will get in one of the pockets, and the number of pocket in which will get in bullet. You have to consider that friction absents, a collision is absolutely resilient, and bullet is a material point.
In the front row, two numbers
1 ≤ M,
N ≤ 2000000000. Numbering Luz clockwise from top left pocket, from which viletel ball, according to the picture.
M - horizontal side of the billiard,
N - the vertical side of the billiard.
Two numbers through gap: the number of reflections of the ball and the number of pockets in which the ball drops.