Laser

Scientists in Byteland have developed a new laser to aid in their research. Before it can be put into practical use, the laser must undergo testing at a secret site in Byteland.

The testing area is a rectangle of size N-1 by M-1 meters, divided into squares of 1\ \mathrm{m}^2 by vertical and horizontal lines. This area can be visualized as a grid with N-1 rows and M-1 columns. The horizontal lines are numbered from bottom to top starting at $1$, and the vertical lines from left to right, also starting at $1$. Thus, each intersection of a vertical and horizontal line (a total of N \times M intersections) can be identified by a pair of numbers (X, Y), which are called the coordinates of the point: $X$ is the vertical line number, and $Y$ is the horizontal line number at the intersection.

The laser is positioned at the coordinates $(A,B)$. At every other intersection point, sensors are installed, which are triggered when the laser beam passes through them. The laser can fire from $(A,B)$ to any other intersection. Only the sensors belonging to the segment with endpoints at the starting coordinates of the laser $(A,B)$ and the chosen target point will be triggered. Note that all sensors and the laser are located on the same plane.

Figure 1. Description of the first example. N = 3,\ M = 6,\ A = 1,\ B = 1

A shot at the point $(5,3)$ triggers the sensors $(3,2)$ and $(5,3)$, while shots at the points $(4,2)$ and $(5,2)$ only trigger the sensors at the endpoints. After shots at all other points, sensors $(2,2)$, $(3,2)$, $(1,2)$, and $(5,1)$ are triggered $2$ times each; sensor $(4,1)$, $3$ times; sensor $(3,1)$, $4$ times; sensor $(2,1)$, $5$ times; and the rest $1$ time each. In total, all sensors are triggered $30$ times.

During the tests, the scientists fire the laser from the starting point $(A,B)$ to every other point on the grid exactly once. Your task is to determine the total number of times all sensors on the testing field are triggered.