{"trustable":true,"sections":[{"title":"","value":{"format":"HTML","content":"\u003cdiv class\u003d\"problem_par\"\u003e\u003cdiv class\u003d\"problem_par_normal\"\u003eLittle boy Vasya likes high-end technologies. Recently he read about \"clever houses\",\r\nwhere everything is managed automatically, and decided to make his house \"clever\".\r\nTo begin with, he connected all \u003ci\u003eN\u003c/i\u003e light-bulbs to his computer, which will help\r\nto manage the lighting level and save the energy.\u003c/div\u003e\u003c/div\u003e\u003cdiv class\u003d\"problem_par\"\u003e\u003cdiv class\u003d\"problem_par_normal\"\u003eLittle hacker Petr, who lives nearby, decided to make a nasty thing to Vasya. He \r\ncreated a computer virus. The main action of this virus is to select a random \r\nlight-bulb and change its state (to switch off if it was on, and vice versa). This\r\naction is repeated for \u003ci\u003eK\u003c/i\u003e times.\u003c/div\u003e\u003c/div\u003e\u003cdiv class\u003d\"problem_par\"\u003e\u003cdiv class\u003d\"problem_par_normal\"\u003eAt the beginning there were \u003ci\u003eM\u003c/i\u003e light bulbs turned on. Now Petr wants to know how efficient his attack will be. More precisely, he wants to know how much light-bulbs in average will be on after the virus is activated (the mathematical expectation of this value). Help him in this complex task!\u003c/div\u003e\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cdiv class\u003d\"problem_par\"\u003e\u003cdiv class\u003d\"problem_par_normal\"\u003eIn the only line there are three integers: \u003ci\u003eN\u003c/i\u003e \u003cnobr\u003e(1 ≤ \u003ci\u003eN\u003c/i\u003e ≤ 10\u003csup\u003e9\u003c/sup\u003e)\u003c/nobr\u003e, \u003ci\u003eM\u003c/i\u003e \u003cnobr\u003e(0 ≤ \u003ci\u003eM\u003c/i\u003e ≤ \u003ci\u003eN\u003c/i\u003e)\u003c/nobr\u003e, \u003ci\u003eK\u003c/i\u003e \u003cnobr\u003e(0 ≤ \u003ci\u003eK\u003c/i\u003e ≤ 1000)\u003c/nobr\u003e.\u003c/div\u003e\u003c/div\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cdiv class\u003d\"problem_par\"\u003e\u003cdiv class\u003d\"problem_par_normal\"\u003eOutput the answer as an irreducible fraction \u003ci\u003ep\u003c/i\u003e/\u003ci\u003eq\u003c/i\u003e.\r\n\u003c/div\u003e\u003c/div\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\u003e1 1 9\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e0/1\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003cbr\u003e\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\u003e5 4 3\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e353/125\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}