{"trustable":false,"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":"Description","value":{"format":"MD","content":"In order to prepare for the coming war against Dr. Jeno, Ishigami Senku wants to test a petrify device. A pertrify device can turn everything in a range of $r$ meters around it into stone. It\u0027s obvious that the \"stone zone\" will be a sphere.\n\nThe device is set with a delay of $t$ seconds, so it will launch at the $t$-th second after being thrown away.\n\nSenku will throw the device in a random direction with initial velocity(speed) of $v\\~ m/s$. He wants to know the probability that he will *not* be turned into stone.\n\nTo check your answer precisely, you should output it modulo $10^9+7$. 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 $0 \\leq x\u003cM$ and $x \\cdot q \\equiv p (mod M)$. \n\nNote that this is a problem in 3D world. The speed has direction, and the acceleration of gravity is $10\\~m/s^2$. The device will not hit anything before it launches, and Senku will not move."}},{"title":"Input","value":{"format":"MD","content":"The input consists of multiple test cases.\n\nThe first line contains an integer $T$ ($1 \\leq T \\leq 10^5$) as the number of test cases.\n\nEach test case contains three integers $t$, $v$ and $r$ ($1 \\leq t,v,r \\leq 100$)."}},{"title":"Output","value":{"format":"MD","content":"For each test case, print the answer modulo $10^9+7$ in a single line."}},{"title":"Sample","value":{"format":"MD","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\u003e\u003cpre\u003e5\n1 10 10\n1 16 10\n1 15 10\n1 4 10\n1 5 10\u003c/pre\u003e\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e\u003cpre\u003e625000005\n1\n1\n0\n0\u003c/pre\u003e\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}