{"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\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":"\u003cp\u003eOur child likes computer science very much, especially he likes binary trees.\u003c/p\u003e\u003cp\u003eConsider the sequence of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e distinct positive integers: \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ec\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e, \u003ci\u003ec\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e, ..., \u003ci\u003ec\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e. The child calls a vertex-weighted rooted binary tree \u003cspan class\u003d\"tex-font-style-it\"\u003egood\u003c/span\u003e if and only if for every vertex \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ev\u003c/i\u003e\u003c/span\u003e, the weight of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ev\u003c/i\u003e\u003c/span\u003e is in the set \u003cspan class\u003d\"tex-span\"\u003e{\u003ci\u003ec\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e, \u003ci\u003ec\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e, ..., \u003ci\u003ec\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e}\u003c/span\u003e. Also our child thinks that the \u003cspan class\u003d\"tex-font-style-it\"\u003eweight\u003c/span\u003e of a vertex-weighted tree is the sum of all vertices\u0027 weights.\u003c/p\u003e\u003cp\u003eGiven an integer \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e, can you for all \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003es\u003c/i\u003e\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e(1 ≤ \u003ci\u003es\u003c/i\u003e ≤ \u003ci\u003em\u003c/i\u003e)\u003c/span\u003e calculate the number of good vertex-weighted rooted binary trees with weight \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003es\u003c/i\u003e\u003c/span\u003e? Please, check the samples for better understanding what trees are considered different.\u003c/p\u003e\u003cp\u003eWe only want to know the answer modulo \u003cspan class\u003d\"tex-span\"\u003e998244353\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e7 × 17 × 2\u003csup class\u003d\"upper-index\"\u003e23\u003c/sup\u003e + 1\u003c/span\u003e, a prime number).\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line contains two integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e, \u003ci\u003em\u003c/i\u003e\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e(1 ≤ \u003ci\u003en\u003c/i\u003e ≤ 10\u003csup class\u003d\"upper-index\"\u003e5\u003c/sup\u003e;\u0026nbsp;1 ≤ \u003ci\u003em\u003c/i\u003e ≤ 10\u003csup class\u003d\"upper-index\"\u003e5\u003c/sup\u003e)\u003c/span\u003e. The second line contains \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e space-separated pairwise distinct integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ec\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e, \u003ci\u003ec\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e, ..., \u003ci\u003ec\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e. \u003cspan class\u003d\"tex-span\"\u003e(1 ≤ \u003ci\u003ec\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e ≤ 10\u003csup class\u003d\"upper-index\"\u003e5\u003c/sup\u003e)\u003c/span\u003e.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003ePrint \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e lines, each line containing a single integer. The \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e-th line must contain the number of good vertex-weighted rooted binary trees whose weight exactly equal to \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e. Print the answers modulo \u003cspan class\u003d\"tex-span\"\u003e998244353\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e7 × 17 × 2\u003csup class\u003d\"upper-index\"\u003e23\u003c/sup\u003e + 1\u003c/span\u003e, a prime number).\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\u003e2 3\n1 2\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1\n3\n9\n\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 10\n9 4 3\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e0\n0\n1\n1\n0\n2\n4\n2\n6\n15\n\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\u003e5 10\n13 10 6 4 15\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e0\n0\n0\n1\n0\n1\n0\n2\n0\n5\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Note","value":{"format":"HTML","content":"\u003cp\u003eIn the first example, there are \u003cspan class\u003d\"tex-span\"\u003e9\u003c/span\u003e good vertex-weighted rooted binary trees whose weight exactly equal to \u003cspan class\u003d\"tex-span\"\u003e3\u003c/span\u003e:\u003c/p\u003e\u003ccenter\u003e \u003cimg class\u003d\"tex-graphics\" src\u003d\"CDN_BASE_URL/1045e8d0892d097c4fb12e94d0b08b09?v\u003d1714596781\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e \u003c/center\u003e"}}]}