{"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\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":"MD","content":"\u003cp\u003eTwilight Sparkle was playing Ludo with her friends Rainbow Dash, Apple Jack and Flutter Shy. But she kept losing. Having returned to the castle, Twilight Sparkle became interested in the dice that were used in the game.\u003c/p\u003e\n\u003cp\u003eThe dice has \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e faces: the first face of the dice contains a dot, the second one contains two dots, and so on, the \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e-th face contains \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e dots. Twilight Sparkle is sure that when the dice is tossed, each face appears with probability $\\frac{1}{m}$. Also she knows that each toss is independent from others. Help her to calculate the expected maximum number of dots she could get after tossing the dice \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e times.\u003c/p\u003e"}},{"title":"Input","value":{"format":"MD","content":"\u003cp\u003eA single line contains two integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003em\u003c/i\u003e, \u003ci\u003en\u003c/i\u003e ≤ 10\u003csup class\u003d\"upper-index\"\u003e5\u003c/sup\u003e\u003c/span\u003e).\u003c/p\u003e"}},{"title":"Output","value":{"format":"MD","content":"\u003cp\u003eOutput a single real number corresponding to the expected maximum. The answer will be considered correct if its relative or absolute error doesn\u0027t exceed \u003cspan class\u003d\"tex-span\"\u003e10 \u003csup class\u003d\"upper-index\"\u003e - 4\u003c/sup\u003e\u003c/span\u003e.\u003c/p\u003e"}},{"title":"Sample 1","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\u003e6 1\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e3.500000000000\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Sample 2","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\u003e6 3\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e4.958333333333\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Sample 3","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\u003e2 2\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1.750000000000\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Note","value":{"format":"MD","content":"\u003cp\u003eConsider the third test example. If you\u0027ve made two tosses:\u003c/p\u003e\n\u003col\u003e \n \u003cli\u003e You can get 1 in the first toss, and 2 in the second. Maximum equals to 2. \u003c/li\u003e\n \u003cli\u003e You can get 1 in the first toss, and 1 in the second. Maximum equals to 1. \u003c/li\u003e\n \u003cli\u003e You can get 2 in the first toss, and 1 in the second. Maximum equals to 2. \u003c/li\u003e\n \u003cli\u003e You can get 2 in the first toss, and 2 in the second. Maximum equals to 2. \u003c/li\u003e\n\u003c/ol\u003e\n\u003cp\u003eThe probability of each outcome is 0.25, that is expectation equals to: \u003c/p\u003e\n\n$$(2+1+2+2) \\cdot 0.25 \u003d \\frac{7}{4}$$\n\n\u003cp\u003eYou can read about expectation using the following link: \u003cspan class\u003d\"tex-font-style-tt\"\u003ehttp://en.wikipedia.org/wiki/Expected_value\u003c/span\u003e\u003c/p\u003e"}}]}