{"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\"We are wasting time, let\u0027s go.\"\u003cbr\u003e\u003cbr\u003e\"Terrorists win.\"\u003cbr\u003e\u003cbr\u003e\"Form up, let\u0027s go.\"\u003cbr\u003e\u003cbr\u003e\"Terrorists win.\"\u003cbr\u003e\u003cbr\u003e......\u003cbr\u003e\u003cbr\u003eAfter being defeated several times, he was so angry that he decided to cheat. He used some tricks to make himself fly really high so that nobody could hurt him. He started to throw grenades, but he suddenly found that he had only 1 hp, which means he would die if the grenade hurt him. Now, Link wants to know the possibility that he will die.\u003cbr\u003e\u003cbr\u003eFormally, there is a grenade with initial speed $v_0$ m/s and explode time $t$ s, which was thrown in a random direction. When the grenade explodes, it will hurt anyone whose distance to it is no more than $r$. Supposing that the grenade didn\u0027t touch anything before explosion, and the man didn\u0027t move after throwing the grenade, you should output the probability that the man will \u003cb\u003esurvive\u003c/b\u003e.\u003cbr\u003e\u003cbr\u003eIn order to check your answer precisely, you should output it modulo $10^9+7$.\u003cbr\u003e\u003cbr\u003e\u003cdiv style\u003d\"font-family:Times New Roman;font-size:14px;background-color:F4FBFF;border:#B7CBFF 1px dashed;padding:6px\"\u003e\u003cdiv style\u003d\"font-family:Arial;font-weight:bold;color:#7CA9ED;border-bottom:#B7CBFF 1px dashed\"\u003e\u003ci\u003eHint\u003c/i\u003e\u003c/div\u003e\u003cbr\u003eNote1: This is a 3D game. In this game, the acceleration of gravity is $10$ $m/s^2$.\u003cbr\u003e\u003cbr\u003eNote2: It can be proved that the answer can always be represented as $\\frac{p}{q}$, where the greatest common factor between $p$ and $q$ is $1$. When outputting the answer modulo $M$, you should output such an integer x that $0 \\leq x \u0026lt; M$ and $ x \\cdot q \\equiv p (mod\\ M) $.\u003cbr\u003e\u003c/div\u003e\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"The input consists of multiple test cases. \u003cbr\u003e\u003cbr\u003eThe first line contains an integer $T$ ($1 \\leq T \\leq 10^5$) -- the number of test cases.\u003cbr\u003e\u003cbr\u003eEach test case contains three integers $t_0,v_0$ and $R$ ($1 \\leq t_0,v_0,R \\leq 100$).\u003cbr\u003e"}},{"title":"Output","value":{"format":"HTML","content":"For each test case, print the answer modulo $10^9+7$ in a single line.\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\u003e5\r\n1 10 10\r\n1 16 10\r\n1 15 10\r\n1 4 10\r\n1 5 10\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e625000005\r\n1\r\n1\r\n0\r\n0\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}