# Signal Interference

Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 512000/512000 K (Java/Others)

## Description

Two countries A-Land and B-Land are at war. The territory of A-Land is a simple polygon with no more than 500 vertices. For military use, A-Land constructed a radio tower (also written as A), and it's so powerful that the whole country was under its signal. To interfere A-Land's communication, B-Land decided to build another radio tower (also written as B). According to an accurate estimation, for any point P, if the euclidean distance between P and B is no more than k (0.2 ≤ k < 0.8) times of the distance between P and A, then point P is not able to receive clear signals from A, i.e. be interfered. Your task is to calculate the area in A-Land's territory that are under B-Land's interference.

## Input

There are no more than 100 test cases in the input.

In each test case, firstly you are given a positive integer N indicating the amount of vertices on A-Land's territory, and an above mentioned real number k, which is rounded to 4 digits after the decimal point.

Then N lines follow. Each line contains two integers x and y (|x|, |y| ≤ 1000), indicating a vertex's coordinate on A's territory, in counterclockwise or clockwise order.

The last two lines of a test case give radio tower A and B's coordinates in the same form as vertexes' coordinates. You can assume that A is not equal to B.

## Output

For each test case, firstly output the case number, then output your answer in one line following the format shown in sample. Please note that there is a blank after the ':'.

Your solution will be accepted if its absolute error or relative error is no more than 10-6.

This problem is special judged.

## Sample Input

4 0.5000
-1 -1
1 -1
1 1
-1 1
0 0
-1 0

## Sample Output

Case 1: 0.2729710441

liuyiding

## Source

2014ACM/ICPC亚洲区广州站-重现赛（感谢华工和北大）