{"trustable":true,"prependHtml":"\u003cscript\u003e window.katexOptions \u003d { disable: true }; \u003c/script\u003e\n\u003cscript type\u003d\"text/x-mathjax-config\"\u003e\n MathJax.Hub.Config({\n tex2jax: {\n inlineMath: [[\u0027$$$\u0027,\u0027$$$\u0027], [\u0027$\u0027,\u0027$\u0027]],\n displayMath: [[\u0027$$$$$$\u0027,\u0027$$$$$$\u0027], [\u0027$$\u0027,\u0027$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS-MML_HTMLorMML\" type\u003d\"text/javascript\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cdiv class\u003d\"panel_content\"\u003e 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\u0027s so powerful that the whole country was under its signal. To interfere A-Land\u0027s 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 \u0026lt; 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\u0027s territory that are under B-Land\u0027s interference. \u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":" There are no more than 100 test cases in the input.\u003cbr\u003e\u003cbr\u003e In each test case, firstly you are given a positive integer N indicating the amount of vertices on A-Land\u0027s territory, and an above mentioned real number k, which is rounded to 4 digits after the decimal point. \u003cbr\u003e\u003cbr\u003e Then N lines follow. Each line contains two integers x and y (|x|, |y| ≤ 1000), indicating a vertex\u0027s coordinate on A\u0027s territory, in counterclockwise or clockwise order. \u003cbr\u003e\u003cbr\u003e The last two lines of a test case give radio tower A and B\u0027s coordinates in the same form as vertexes\u0027 coordinates. You can assume that A is not equal to B. "}},{"title":"Output","value":{"format":"HTML","content":" 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 \u0027:\u0027.\u003cbr\u003e\u003cbr\u003e Your solution will be accepted if its absolute error or relative error is no more than 10-6.\u003cbr\u003e\u003cbr\u003e This problem is special judged."}},{"title":"Sample","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e4 0.5000\r\n-1 -1\r\n1 -1\r\n1 1\r\n-1 1\r\n0 0\r\n-1 0\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eCase 1: 0.2729710441\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}