{"trustable":true,"sections":[{"title":"","value":{"format":"HTML","content":"\u003ch2\u003eProblem J\n\n\u003c/h2\u003e\n\n\u003cp\u003e\nA convex polygon is drawn on a flat paper sheet. You are trying to place a disk in your hands to cover as large area of the polygon as possible. In other words, the intersection area of the polygon and the disk should be maximized.\n\u003c/p\u003e\n\n\n\u003ch3\u003eInput\u003c/h3\u003e\n\n\u003cp\u003e\nThe input consists of a single test case, formatted as follows. All input items are integers.\u003cbr\u003e\n\u003cbr\u003e\n$n$ $r$\u003cbr\u003e\n$x_1$ $y_1$\u003cbr\u003e\n.\u003cbr\u003e\n.\u003cbr\u003e\n.\u003cbr\u003e\n$x_n$ $y_n$\u003cbr\u003e\n\u003c/p\u003e\n\n\u003cp\u003e\n$n$ is the number of vertices of the polygon ($3 \\leq n \\leq 10$). $r$ is the radius of the disk ($1 \\leq r \\leq 100$).\n$x_i$ and $y_i$ give the coordinate values of the $i$-th vertex of the polygon ($1 \\leq i \\leq n$). Coordinate values satisfy $0 \\leq x_i \\leq 100$ and $0 \\leq y_i \\leq 100$.\n\u003c/p\u003e\n\n\u003cp\u003e\nThe vertices are given in counterclockwise order. As stated above, the given polygon is convex. In other words, interior angles at all of its vertices are less than 180$^{\\circ}$. Note that the border of a convex polygon never crosses or touches itself.\n\u003c/p\u003e\n\n\n\n\u003ch3\u003eOutput\u003c/h3\u003e\n\n\u003cp\u003e\nOutput the largest possible intersection area of the polygon and the disk. The answer should not have an error greater than 0.0001 ($10^{-4}$).\n\u003c/p\u003e\n\n\n\u003ch3\u003eSample Input 1\u003c/h3\u003e\n\n\u003cpre\u003e4 4\n0 0\n6 0\n6 6\n0 6\u003c/pre\u003e\n\n\u003ch3\u003eSample Output 1\u003c/h3\u003e\n\n\u003cpre\u003e35.759506\u003c/pre\u003e\n\n\u003cbr\u003e\n\n\u003ch3\u003eSample Input 2\u003c/h3\u003e\n\n\u003cpre\u003e3 1\n0 0\n2 1\n1 3\u003c/pre\u003e\n\n\u003ch3\u003eSample Output 2\u003c/h3\u003e\n\n\u003cpre\u003e2.113100\u003c/pre\u003e\n\n\u003cbr\u003e\n\n\u003ch3\u003eSample Input 3\u003c/h3\u003e\n\n\u003cpre\u003e3 1\n0 0\n100 1\n99 1\u003c/pre\u003e\n\n\u003ch3\u003eSample Output 3\u003c/h3\u003e\n\n\u003cpre\u003e0.019798\u003c/pre\u003e\n\n\u003cbr\u003e\n\n\u003ch3\u003eSample Input 4\u003c/h3\u003e\n\n\u003cpre\u003e4 1\n0 0\n100 10\n100 12\n0 1\u003c/pre\u003e\n\n\u003ch3\u003eSample Output 4\u003c/h3\u003e\n\n\u003cpre\u003e3.137569\u003c/pre\u003e\n\n\u003cbr\u003e\n\n\u003ch3\u003eSample Input 5\u003c/h3\u003e\n\n\u003cpre\u003e10 10\n0 0\n10 0\n20 1\n30 3\n40 6\n50 10\n60 15\n70 21\n80 28\n90 36\u003c/pre\u003e\n\n\u003ch3\u003eSample Output 5\u003c/h3\u003e\n\n\u003cpre\u003e177.728187\u003c/pre\u003e\n\n\n\n\u003cbr\u003e\n\n\u003ch3\u003eSample Input 6\u003c/h3\u003e\n\n\u003cpre\u003e10 49\n50 0\n79 10\n96 32\n96 68\n79 90\n50 100\n21 90\n4 68\n4 32\n21 10\u003c/pre\u003e\n\n\u003ch3\u003eSample Output 6\u003c/h3\u003e\n\n\u003cpre\u003e7181.603297\u003c/pre\u003e\n\n\n\n\n\n\n\n\n\n"}}]}