Save the Dinosaurs

Breaking news from Bytetown: palaeontologists have discovered the fossil remains of dinosaurs near the city! On hearing the news, several citizens rushed to grab a bone or two for themselves. To protect these priceless remains, the mayor of Bytetown decided to guard the excavation area and hired the army for the task.

General Byteasar has stationed $n$ soldiers at several strategic positions of the excavation area. A point of the area is said to be protected if moving away from that point in any direction unavoidably decreases the distance to at least one of the soldiers.

The general has just been assigned a new rookie soldier. He wants to place this soldier in one of the $m$ still-vacant strategic positions. For each possible placement he would like to know the total area of the protected part of the excavations.

The first line contains two integers $n$ and $m$ ($3 \le n \le 100\,000$, $1 \le m \le 100\,000$): the number of soldiers already stationed and the number of vacant strategic positions.

Each of the next $n$ lines describes a soldier's position: the $i$-th of them contains two integers $x_i$ and $y_i$ ($-10^8 \le x_i, y_i \le 10^8$), the coordinates of the $i$-th soldier in a rectangular coordinate system.

Each of the following $m$ lines describes, in the same format, a vacant strategic position. All points given in the input are distinct.

You may assume that the area protected by the $n$ soldiers is positive.

Output exactly $m$ lines. The $i$-th line should contain the total area of the protected part of the excavations after the rookie soldier is placed at the $i$-th vacant strategic position. Every number must be printed with exactly one digit after the decimal point.