Farmer John has recently acquired a nice herd of N goats for his field. Each goat i
will be tied to a pole at some position P_{i} using a rope of length L_{i}. This means that the goat will be able to travel anywhere in the field that is within distance L_{i} of the point P_{i}, but nowhere else. (The field is large and flat, so you can think of it as an infinite twodimensional plane.)
Farmer John already has the pole positions picked out from his last herd of goats, but he has to choose the rope lengths. There are two factors that make this decision tricky:
Unfortunately, Farmer John is not very good at geometry, and he needs your help for this part!
For each bucket position Q_{j}, you should choose rope lengths so as to minimize the area A_{j} that can be reached by every goat when the bucket is located at position Q_{j}. You should then calculate each of these areas A_{j}.
In the picture below, there are four blue points, corresponding to the pole positions: P_{1}, P_{2}, P_{3}, and P_{4}. There are also two red points, corresponding to the potential bucket positions: Q_{1} and Q_{2}. You need to calculate A_{1} and A_{2}, the areas of the two shaded regions.
The first line of the input gives the number of test cases, T. T test cases follow. Each test case begins with a line containing the integers N and M.
The next N lines contain the positions P_{1}, P_{2}, ..., P_{N}, one per line. This is followed by M lines, containing the positions Q_{1}, Q_{2}, ..., Q_{M}, one per line.
Each of these N + M lines contains the corresponding position's x and y coordinates, separated by a single space.
For each test case, output one line containing "Case #x: A_{1} A_{2} ... A_{M}", where x is the case number (starting from 1), and A_{1} A_{2} ... A_{M} are the values defined above. Answers with a relative or absolute error of at most 10^{6} will be considered correct.
All coordinates are integers between 10,000 and 10,000.
The positions P_{1}, P_{2}, ..., P_{N}, Q_{1}, Q_{2}, ..., Q_{M} are all distinct and no three are collinear.
1 ≤ T ≤ 100.
N = 2.
1 ≤ M ≤ 10.
1 ≤ T ≤ 10.
2 ≤ N ≤ 5,000.
1 ≤ M ≤ 1,000.
Input 
Output 
1

Case #1: 1264.9865911 1713.2741229 0.2939440

Input 
Output 
2

Case #1: 1518.9063729 1193932.9692206

Points  Correct  Attempted 

7pt  194  333 
25pt  2  11 