Shooting Range

Vasya, a student, decided to spend his summer vacation in a resort town. During an evening walk along the promenade, he came across many attractions designed to entertain vacationers and make money. Most of these were various kinds of shooting galleries, ranging from throwing darts at inflatable balloons to shooting at tin cans with air guns. Prizes were given for accurate shots (often their value was even less than the cost of playing). Vasya noticed that at some attractions the promoters cheated (for example, by slightly disaligning the air rifle sights), while at others they played fairly and even sometimes gave extra shots to players, especially children. These relatively honest attractions gathered noticeably more people, and Vasya realized that thanks to the higher turnover, "honest" shooting galleries probably generated more profit. So Vasya decided to earn money as well. He invented a computer-based shooting gallery whose fairness would not be in doubt among players.

The target in the shooting gallery is a touch panel made up of squares measuring 1 \times 1 cm, $N$ squares vertically and $M$ squares horizontally. When a plastic pellet from an air pistol hits the panel, the connected computer receives the impact coordinates (in centimeters) as two non-negative real numbers, specified to one-tenth of a millimeter, with the origin at the top-left corner of the panel. The computer screen displays the numbers of the prize cells the player can open. The cell numbers correspond uniquely to the panel's squares and are numbered sequentially from left to right, top to bottom, with the first cell being number $1$ and the last being N \cdot M. If the pellet hits the boundary between two cells, both cell numbers are shown (if exactly at a corner, on the boundary of four cells, all four numbers are shown). Help Vasya carry out his idea by writing software for the shooting gallery.