Football 2
On a football field with dimensions x × y, there are n football players. These players are currently stationary, waiting to see where the ball will land so they can run towards it. A player will run to the ball if it lands closer to them than to any other player.
Your task is to determine the boundaries of the zone for each player, within which they will run to the ball. This zone forms a polygon.
Input
The first line of the input contains three integers: x, y, and n (2 ≤ x, y ≤ 10^5, 1 ≤ n ≤ 30000). The following n lines each contain the integer coordinates of a player, x_i y_i (0 < x_i < x, 0 < y_i < y). No two players occupy the same position.
Output
Output n lines. Each line should start with the number of vertices of the zone, k_i, followed by k_i pairs of numbers representing the coordinates of the vertices, x_ij y_ij, listed in counterclockwise order starting from the vertex with the smallest x-coordinate (and smallest y-coordinate in case of a tie). Output the coordinates as real numbers with maximum precision.