{"trustable":true,"prependHtml":"\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 async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS-MML_HTMLorMML\" type\u003d\"text/javascript\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cdiv class\u003d\"panel_content\"\u003eFinal Exam is coming! Cuber QQ has now one night to prepare for tomorrow\u0027s exam.\u003cbr\u003e\u003cbr\u003eThe exam will be a exam of problems sharing altogether $m$ points. Cuber QQ doesn\u0027t know about the exact distribution. Of course, different problems might have different points; in some extreme cases, some problems might worth $0$ points, or all $m$ points. Points must be integers; a problem cannot have $0.5$ point.\u003cbr\u003e\u003cbr\u003eWhat he knows, is that, these $n$ problems will be about $n$ totally different topics. For example, one could be testing your understanding of Dynamic Programming, another might be about history of China in 19th century. So he has to divide your night to prepare each of these topics separately. Also, if one problem is worth $x$ points in tomorrow\u0027s exam, it takes at least $x+1$ hours to prepare everything you need for examination. If he spends less than $x+1$ hours preparing, he shall fail at this problem.\u003cbr\u003e\u003cbr\u003eCuber QQ\u0027s goal, strangely, is not to take as much points as possible, but to solve at least $k$ problems no matter how the examination paper looks like, to get away from his parents\u0027 scoldings. So he wonders how many hours at least he needs to achieve this goal.\u003cbr\u003e\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"The first line of the input is an integer $t$ ($1 \\le t \\le 20~000$), denoting the number of test cases.\u003cbr\u003e\u003cbr\u003eEach test case are three space-separated integers $n,m,k$ ($0 \\le m \\le 10^9$, $1 \\le k \\le n \\le 10^9$). \u003cbr\u003e"}},{"title":"Output","value":{"format":"HTML","content":"For each test case, output the number of hours Cuber QQ needs.\u003cbr\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\u003e2\r\n1 10 1\r\n10 109 10\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e11\r\n1100\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Hint","value":{"format":"HTML","content":"\u003cbr\u003eCuber QQ should solve one problem in sample 1, so he at least prepares 11 hours when the problem one is 10 point. \u003cbr\u003eCuber QQ should solve all the ten problems in sample 2, so he at least prepares 110 hours for each problem because there may be one problem is 109 point.\u003cbr\u003e"}}]}