{"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\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$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript type\u003d\"text/javascript\" async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS_HTML-full\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cstyle type\u003d\u0027text/css\u0027\u003e .input, .output {border: 1px solid #888888;} .output {margin-bottom:1em;position:relative;top:-1px;} .output pre,.input pre {background-color:#EFEFEF;line-height:1.25em;margin:0;padding:0.25em;} .title {background-color:#FFFFFF;border-bottom: 1px solid #888888;font-family:arial;font-weight:bold;padding:0.25em;} \u003c/style\u003e \u003cscript type\u003d\"text/x-mathjax-config\"\u003e\n MathJax.Hub.Config({\n tex2jax: {inlineMath: [[\u0027$$$\u0027,\u0027$$$\u0027]], displayMath: [[\u0027$$$$$$\u0027,\u0027$$$$$$\u0027]]}\n });\n \u003c/script\u003e\n \u003cscript type\u003d\"text/javascript\" async\n src\u003d\"https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config\u003dTeX-AMS-MML_HTMLorMML\"\u003e\n \u003c/script\u003e\n\u003cp\u003ePolandBall is standing in a row with Many Other Balls. More precisely, there are exactly \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e Balls. Balls are proud of their home land\u0026nbsp;— and they want to prove that it\u0027s strong.\u003c/p\u003e\n\u003cp\u003eThe Balls decided to start with selecting exactly \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e groups of Balls, each consisting either of single Ball or two neighboring Balls. Each Ball can join no more than one group.\u003c/p\u003e\n\u003cp\u003eThe Balls really want to impress their Enemies. They kindly asked you to calculate number of such divisions for all \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e where \u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003em\u003c/i\u003e ≤ \u003ci\u003ek\u003c/i\u003e\u003c/span\u003e. Output all these values modulo \u003cspan class\u003d\"tex-span\"\u003e998244353\u003c/span\u003e, the Enemies will be impressed anyway.\u003c/p\u003e\n有一排 n 个球,定义一个组可以只包含一个球或者包含两个相邻的球。现在一个球只能分到一个组中,求从这些球中取出 k 组的方案数。n≤10^9,k\u003c2^15 。"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThere are exactly two numbers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\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\u003en\u003c/i\u003e ≤ 10\u003csup class\u003d\"upper-index\"\u003e9\u003c/sup\u003e\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003ek\u003c/i\u003e \u0026lt; 2\u003csup class\u003d\"upper-index\"\u003e15\u003c/sup\u003e\u003c/span\u003e), denoting the number of Balls and the maximim number of groups, respectively.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eYou should output a sequence of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e values. The \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e-th of them should represent the sought number of divisions into exactly \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e groups, according to PolandBall\u0027s rules.\u003c/p\u003e"}},{"title":"Examples","value":{"format":"HTML","content":"\u003cdiv class\u003d\"sample-test\"\u003e\n \u003cdiv class\u003d\"input\"\u003e\n \u003cdiv class\u003d\"title\"\u003e\n Input\n \u003c/div\u003e\n \u003cpre\u003e3 3\u003cbr\u003e\u003c/pre\u003e\n \u003c/div\u003e\n \u003cdiv class\u003d\"output\"\u003e\n \u003cdiv class\u003d\"title\"\u003e\n Output\n \u003c/div\u003e\n \u003cpre\u003e5 5 1 \u003c/pre\u003e\n \u003c/div\u003e\n \u003cdiv class\u003d\"input\"\u003e\n \u003cdiv class\u003d\"title\"\u003e\n Input\n \u003c/div\u003e\n \u003cpre\u003e1 1\u003cbr\u003e\u003c/pre\u003e\n \u003c/div\u003e\n \u003cdiv class\u003d\"output\"\u003e\n \u003cdiv class\u003d\"title\"\u003e\n Output\n \u003c/div\u003e\n \u003cpre\u003e1 \u003c/pre\u003e\n \u003c/div\u003e\n \u003cdiv class\u003d\"input\"\u003e\n \u003cdiv class\u003d\"title\"\u003e\n Input\n \u003c/div\u003e\n \u003cpre\u003e5 10\u003cbr\u003e\u003c/pre\u003e\n \u003c/div\u003e\n \u003cdiv class\u003d\"output\"\u003e\n \u003cdiv class\u003d\"title\"\u003e\n Output\n \u003c/div\u003e\n \u003cpre\u003e9 25 25 9 1 0 0 0 0 0 \u003c/pre\u003e\n \u003c/div\u003e\n\u003c/div\u003e"}},{"title":"Note","value":{"format":"HTML","content":"\u003cp\u003eIn the first sample case we can divide Balls into groups as follows: \u003c/p\u003e\n\u003cp\u003e\u003cspan class\u003d\"tex-span\"\u003e{1}\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e{2}\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e{3}\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e{12}\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e{23}\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003e\u003cspan class\u003d\"tex-span\"\u003e{12}{3}\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e{1}{23}\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e{1}{2}\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e{1}{3}\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e{2}{3}\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003e\u003cspan class\u003d\"tex-span\"\u003e{1}{2}{3}\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003eTherefore, output is: \u003cspan class\u003d\"tex-font-style-tt\"\u003e5 5 1\u003c/span\u003e.\u003c/p\u003e"}}]}