{"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\n\u003cscript\u003e\n window.katexOptions \u003d {\n delimiters: [\n {left: \u0027$$$$$$\u0027, right: \u0027$$$$$$\u0027, display: true},\n {left: \u0027$$$\u0027, right: \u0027$$$\u0027, display: false},\n {left: \u0027$$\u0027, right: \u0027$$\u0027, display: true},\n {left: \u0027$\u0027, right: \u0027$\u0027, display: false}\n ]\n };\n\u003c/script\u003e\n","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eThere are \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e casinos lined in a row. If Memory plays at casino \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e, he has probability \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ep\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e to win and move to the casino on the right (\u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e + 1\u003c/span\u003e) or exit the row (if \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e \u003d \u003ci\u003en\u003c/i\u003e\u003c/span\u003e), and a probability \u003cspan class\u003d\"tex-span\"\u003e1 - \u003ci\u003ep\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e to lose and move to the casino on the left (\u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e - 1\u003c/span\u003e) or also exit the row (if \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e \u003d 1\u003c/span\u003e). \u003c/p\u003e\u003cp\u003eWe say that Memory \u003cspan class\u003d\"tex-font-style-it\"\u003edominates\u003c/span\u003e on the interval \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e... \u003ci\u003ej\u003c/i\u003e\u003c/span\u003e if he completes a walk such that,\u003c/p\u003e\u003cul\u003e \u003cli\u003e He starts on casino \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e. \u003c/li\u003e\u003cli\u003e He never looses in casino \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e. \u003c/li\u003e\u003cli\u003e He finishes his walk by winning in casino \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ej\u003c/i\u003e\u003c/span\u003e. \u003c/li\u003e\u003c/ul\u003e\u003cp\u003eNote that Memory can still walk left of the \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e-st casino and right of the casino \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e and that always finishes the process.\u003c/p\u003e\u003cp\u003eNow Memory has some requests, in one of the following forms:\u003c/p\u003e\u003cul\u003e \u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eb\u003c/i\u003e\u003c/span\u003e: Set \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/24e67b9332601ce65490953296072272?v\u003d1726411673\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e. \u003c/li\u003e\u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e2\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003el\u003c/i\u003e\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003er\u003c/i\u003e\u003c/span\u003e: Print the probability that Memory will \u003cspan class\u003d\"tex-font-style-it\"\u003edominate\u003c/span\u003e on the interval \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003el\u003c/i\u003e... \u003ci\u003er\u003c/i\u003e\u003c/span\u003e, i.e. compute the probability that Memory will first leave the segment \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003el\u003c/i\u003e... \u003ci\u003er\u003c/i\u003e\u003c/span\u003e after winning at casino \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003er\u003c/i\u003e\u003c/span\u003e, if she starts in casino \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003el\u003c/i\u003e\u003c/span\u003e. \u003c/li\u003e\u003c/ul\u003e\u003cp\u003eIt is guaranteed that at any moment of time \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ep\u003c/i\u003e\u003c/span\u003e is a \u003cspan class\u003d\"tex-font-style-bf\"\u003enon-decreasing sequence\u003c/span\u003e, i.e. \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ep\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e ≤ \u003ci\u003ep\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e + 1\u003c/sub\u003e\u003c/span\u003e for all \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e from \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e to \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e - 1\u003c/span\u003e.\u003c/p\u003e\u003cp\u003ePlease help Memory by answering all his requests!\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line of the input contains two integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eq\u003c/i\u003e\u003c/span\u003e(\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003en\u003c/i\u003e, \u003ci\u003eq\u003c/i\u003e ≤ 100 000\u003c/span\u003e), \u0026nbsp;— number of casinos and number of requests respectively.\u003c/p\u003e\u003cp\u003eThe next \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e lines each contain integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eb\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e \u0026lt; \u003ci\u003eb\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e ≤ 10\u003csup class\u003d\"upper-index\"\u003e9\u003c/sup\u003e\u003c/span\u003e) \u0026nbsp;— \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/8e1e2395c46dde3c5b0be0a4517cfe72?v\u003d1726411673\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e is the probability \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ep\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e of winning in casino \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eThe next \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eq\u003c/i\u003e\u003c/span\u003e lines each contain queries of one of the types specified above (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003ea\u003c/i\u003e \u0026lt; \u003ci\u003eb\u003c/i\u003e ≤ 10\u003csup class\u003d\"upper-index\"\u003e9\u003c/sup\u003e\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003ei\u003c/i\u003e ≤ \u003ci\u003en\u003c/i\u003e\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003el\u003c/i\u003e ≤ \u003ci\u003er\u003c/i\u003e ≤ \u003ci\u003en\u003c/i\u003e\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eIt\u0027s guaranteed that there will be at least one query of type \u003cspan class\u003d\"tex-span\"\u003e2\u003c/span\u003e, i.e. the output will be non-empty. Additionally, it is guaranteed that \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ep\u003c/i\u003e\u003c/span\u003e forms a non-decreasing sequence at all times.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003ePrint a real number for every request of type \u003cspan class\u003d\"tex-span\"\u003e2\u003c/span\u003e\u0026nbsp;— the probability that boy will \"dominate\" on that interval. Your answer will be considered correct if its absolute error does not exceed \u003cspan class\u003d\"tex-span\"\u003e10\u003csup class\u003d\"upper-index\"\u003e - 4\u003c/sup\u003e\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eNamely: let\u0027s assume that one of your answers is \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003c/span\u003e, and the corresponding answer of the jury is \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eb\u003c/i\u003e\u003c/span\u003e. The checker program will consider your answer correct if \u003cspan class\u003d\"tex-span\"\u003e|\u003ci\u003ea\u003c/i\u003e - \u003ci\u003eb\u003c/i\u003e| ≤ 10\u003csup class\u003d\"upper-index\"\u003e - 4\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\u003e3 13\n1 3\n1 2\n2 3\n2 1 1\n2 1 2\n2 1 3\n2 2 2\n2 2 3\n2 3 3\n1 2 2 3\n2 1 1\n2 1 2\n2 1 3\n2 2 2\n2 2 3\n2 3 3\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e0.3333333333\n0.2000000000\n0.1666666667\n0.5000000000\n0.4000000000\n0.6666666667\n0.3333333333\n0.2500000000\n0.2222222222\n0.6666666667\n0.5714285714\n0.6666666667\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}