{"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\"\u003eEdward is a worker for Aluminum Cyclic Machinery. His work is operating mechanical arms to cut out designed models. Here is a brief introduction of his work.\u003cbr\u003eAssume the operating plane as a two-dimensional coordinate system. At first, there is a disc with center coordinates $(0, 0)$ and radius $R$. Then, $m$ mechanical arms will cut and erase everything within its area of influence simultaneously, the $i$-th area of which is a circle with center coordinates $(x_i, y_i)$ and radius $r_i$ $(i \u003d 1, 2, \\cdots, m)$. In order to obtain considerable models, it is guaranteed that every two cutting areas have no intersection and no cutting area contains the whole disc.\u003cbr\u003eYour task is to determine the perimeter of the remaining area of the disc excluding internal perimeter.\u003cbr\u003eHere is an illustration of the sample, in which the red curve is counted but the green curve is not.\u003cbr\u003e\u003ccenter\u003e\u003cimg style\u003d\"max-width:100%;\" src\u003d\"CDN_BASE_URL/0ff0b181470c4bb4f1fb061655fb4ea8?v\u003d1714568150\"\u003e\u003c/center\u003e\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"The first line contains one integer $T$, indicating the number of test cases.\u003cbr\u003eThe following lines describe all the test cases. For each test case:\u003cbr\u003eThe first line contains two integers $m$ and $R$.\u003cbr\u003eThe $i$-th line of the following $m$ lines contains three integers $x_i, y_i$ and $r_i$, indicating a cutting area.\u003cbr\u003e$1 \\leq T \\leq 1000$, $1 \\leq m \\leq 100$, $-1000 \\leq x_i, y_i \\leq 1000$, $1 \\leq R, r_i \\leq 1000$ $(i \u003d 1, 2, \\cdots, m)$."}},{"title":"Output","value":{"format":"HTML","content":"For each test case, print the perimeter of the remaining area in one line. Your answer is considered correct if its absolute or relative error does not exceed $10^{-6}$.\u003cbr\u003eFormally, let your answer be $a$ and the jury\u0027s answer be $b$. Your answer is considered correct if $\\frac{|a - b|}{\\max(1, |b|)} \\leq 10^{-6}$.\u003cbr\u003e"}},{"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\u003e1\r\n4 10\r\n6 3 5\r\n10 -4 3\r\n-2 -4 4\r\n0 9 1\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e81.62198908430238475376\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}