{"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\u003eA new Berland businessman Vitaly is going to open a household appliances\u0027 store. All he\u0027s got to do now is to hire the staff.\u003c/p\u003e\u003cp\u003eThe store will work seven days a week, but not around the clock. Every day at least \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e people must work in the store.\u003c/p\u003e\u003cp\u003eBerland has a law that determines the order of working days and non-working days. Namely, each employee must work for exactly \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e consecutive days, then rest for exactly \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e days, then work for \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e more days and rest for \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e more, and so on. Vitaly doesn\u0027t want to break the law. Fortunately, there is a loophole: the law comes into force on the day when the employee is hired. For example, if an employee is hired on day \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003c/span\u003e, then he should work on days \u003cspan class\u003d\"tex-span\"\u003e[\u003ci\u003ex\u003c/i\u003e, \u003ci\u003ex\u003c/i\u003e + 1, ..., \u003ci\u003ex\u003c/i\u003e + \u003ci\u003en\u003c/i\u003e - 1]\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e[\u003ci\u003ex\u003c/i\u003e + \u003ci\u003em\u003c/i\u003e + \u003ci\u003en\u003c/i\u003e, \u003ci\u003ex\u003c/i\u003e + \u003ci\u003em\u003c/i\u003e + \u003ci\u003en\u003c/i\u003e + 1, ..., \u003ci\u003ex\u003c/i\u003e + \u003ci\u003em\u003c/i\u003e + 2\u003ci\u003en\u003c/i\u003e - 1]\u003c/span\u003e, and so on. Day \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003c/span\u003e can be chosen arbitrarily by Vitaly.\u003c/p\u003e\u003cp\u003eThere is one more thing: the key to the store. Berland law prohibits making copies of keys, so there is only one key. Vitaly is planning to entrust the key to the store employees. At the same time on each day the key must be with an employee who works that day — otherwise on this day no one can get inside the store. During the day the key holder can give the key to another employee, if he also works that day. The key will handed to the first hired employee at his first working day.\u003c/p\u003e\u003cp\u003eEach employee has to be paid salary. Therefore, Vitaly wants to hire as few employees as possible provided that the store can operate normally on each day from \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e to infinity. In other words, on each day with index from \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e to infinity, the store must have at least \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e working employees, and one of the working employees should have the key to the store.\u003c/p\u003e\u003cp\u003eHelp Vitaly and determine the minimum required number of employees, as well as days on which they should be hired.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line contains three integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003em\u003c/i\u003e ≤ \u003ci\u003en\u003c/i\u003e ≤ 1000\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e ≠ 1\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003ek\u003c/i\u003e ≤ 1000\u003c/span\u003e).\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eIn the first line print a single integer \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ez\u003c/i\u003e\u003c/span\u003e — the minimum required number of employees.\u003c/p\u003e\u003cp\u003eIn the second line print \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ez\u003c/i\u003e\u003c/span\u003e positive integers, separated by spaces: the \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e-th integer \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 (\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 ≤ 10\u003csup class\u003d\"upper-index\"\u003e4\u003c/sup\u003e\u003c/span\u003e) should represent the number of the day, on which Vitaly should hire the \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e-th employee.\u003c/p\u003e\u003cp\u003eIf there are multiple answers, print any of them.\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\u003e4 3 2\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e4\n1 1 4 5\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"","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 3 1\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e3\n1 3 5\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}