{"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\"\u003eJenny is seriously drunk. He feels as if he is in an N-dimension Euclidean space, wandering aimlessly. In each step, he walks toward some direction and the “length” of each step will not exceed R. Technically speaking, Jenny is initially located at the origin of the N-dimension Euclidean space. Each step can be represented by a random N-dimension vector(x\u003csub\u003e1\u003c/sub\u003e, x\u003csub\u003e2\u003c/sub\u003e, ... , x\u003csub\u003en\u003c/sub\u003e) chosen uniformly from possible positions satisfying x\u003csub\u003ei\u003c/sub\u003e \u0026gt;\u003d 0 and x\u003csub\u003e1\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e + x\u003csub\u003e2\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e + ... \u0026lt;\u003d R\u003csup\u003e2\u003c/sup\u003e.\u003cbr\u003eAssume the expectation of his coordinate after his first step is (y\u003csub\u003e1\u003c/sub\u003e, y\u003csub\u003e2\u003c/sub\u003e, ... , y\u003csub\u003en\u003c/sub\u003e). He wants to know the minimum y\u003csub\u003ei\u003c/sub\u003e .\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"There are several (about 100,000) test cases, please process till EOF.\u003cbr\u003eEach test case, only one line contains two integers N and R, representing the dimension of the space and the length limit of each step.(1 \u0026lt;\u003d n \u0026lt;\u003d 2 * 10\u003csup\u003e5\u003c/sup\u003e, R \u0026lt;\u003d 10\u003csup\u003e5\u003c/sup\u003e)."}},{"title":"Output","value":{"format":"HTML","content":"For each test case, print a real number representing the answer to the question above. \u003cbr\u003eYour answer is considered correct if the difference between your answer and the correct one is less than 10\u003csup\u003e-6\u003c/sup\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\u003e2 1\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e0.4244131816\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}