{"trustable":false,"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":"MD","content":"Easy Access Inc. (EA) is a video game company. They often offer loot boxes that you have to buy with actual money to gain some in-game benefits. On one hand, these loot boxes promote a pay-to-win culture among players that leapfrog their way through the game ruining the actual fun. On the other hand, even the loot boxes are not fair.\n\nConsider that, there are **K** loot boxes. Each box can contain any number of good or bad items from EA. A player randomly chooses one loot box from those **K** boxes. Let\u0027s say there are *X* items inside that loot box. The player is shown *X* cards. All cards look the same. Each card is associated with one item in the box. The player then randomly chooses one of those *X* cards. After that, the item associated with the card is revealed to the player.\n\nThere are **N** good items and **M** bad items distributed among these **K** loot boxes. Now EA, being an evil company, will distribute the items in such a way that the probability of a player picking a bad item is maximized.\n\nYour task is to determine the worst possible arrangement of items and find out the probability that a player will pick a bad item."}},{"title":"Input","value":{"format":"MD","content":"The input consists of three space-separated integers **N**, **M**, and **K** **(1 ≤ N, M, K ≤ 10\u003csup\u003e9\u003c/sup\u003e)**, denoting the number of good items, the number of bad items, and the number of loot boxes, respectively."}},{"title":"Output","value":{"format":"MD","content":"Print the probability of a player getting a bad item in an optimal evil arrangement. Absolute errors less than 10\u003csup\u003e-6\u003c/sup\u003e will be ignored."}},{"title":"Sample Input","value":{"format":"MD","content":"```\n50 50 2\n```"}},{"title":"Sample Output","value":{"format":"MD","content":"```\n0.747474747\n```"}}]}