{"trustable":true,"prependHtml":"\u003cstyle type\u003d\u0027text/css\u0027\u003e\n .input, .output {\n border: 1px solid #888888;\n }\n .output {\n margin-bottom: 1em;\n position: relative;\n top: -1px;\n }\n .output pre, .input pre {\n background-color: #EFEFEF;\n line-height: 1.25em;\n margin: 0;\n padding: 0.25em;\n }\n \u003c/style\u003e\n \u003clink rel\u003d\"stylesheet\" href\u003d\"//codeforces.org/s/96598/css/problem-statement.css\" type\u003d\"text/css\" /\u003e\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 type\u003d\"text/javascript\" async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS_HTML-full\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eJuan have N red marbles, M blue marbles, and K bottles. He will put a certain number of marbles on each of the K bottles such that no bottle remains empty and every marble is inside a bottle.\u003c/p\u003e\u003cp\u003eAndres is a Santa Fe fan, so he will pick one bottle at random with an uniform distribution, then he will pick a marble inside of it at random with an uniform distribution, with the hope is a red marble. As Juan is a Millonarios fan, he wants to distribute the marbles in the bottles such that the probability of Andres picking a blue marble is maximized. Juan has a busy life, therefore he needs your help to determine the best arrangement for the marbles and the probability of Andres getting a blue marble. \u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe input consist of three integers separated by spaces, N M and K (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003eN\u003c/i\u003e, \u003ci\u003eM\u003c/i\u003e, \u003ci\u003eK\u003c/i\u003e ≤ 10\u003csup class\u003d\"upper-index\"\u003e9\u003c/sup\u003e\u003c/span\u003e) - the number of red marbles, blue marbles and bottles respectively.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003ePrint the probability of Bob getting a blue marble such that the marble arrangement is optimal. Your answer will be considered correct, if its absolute or relative error does not exceed \u003cspan class\u003d\"tex-span\"\u003e10\u003csup class\u003d\"upper-index\"\u003e - 6\u003c/sup\u003e\u003c/span\u003e.\u003c/p\u003e"}},{"title":"Examples","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\u003e50 50 2\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e0.747474747\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}