{"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$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript type\u003d\"text/javascript\" async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS_HTML-full\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eAlex is proud of the holy sequence.\u003c/p\u003e\u003cp\u003eAlex thinks that a sequence $$$a_1,a_2,\\cdots, a_n$$$ is $$$n$$$-holy if and only if\u003c/p\u003e\u003cul\u003e \u003cli\u003e For each $$$i \\in [1,n]$$$, $$$a_i \\in \\{1,2,\\cdots, n\\}$$$ ; \u003c/li\u003e\u003cli\u003e For each $$$i \\in [1,n]$$$, $$$p_i - p_{i-1} \\le 1$$$ ($$$p_k \u003d \\max\\{a_1,a_2,\\cdots, a_k\\}$$$, $$$p_0\u003d0$$$). \u003c/li\u003e\u003c/ul\u003e\u003cp\u003eFor each $$$t \u003d 1,2, \\cdots, n$$$, Alex wants to know $$$$$$ \\sum_{p \\in S_n} \\mathrm{cnt}(p,t)^2, $$$$$$ where $$$S_n$$$ is the set of all $$$n$$$-holy sequences and $$$\\mathrm{cnt}(p,t)$$$ is the occurrence number of $$$t$$$ in sequence $$$p$$$. \u003c/p\u003e\u003cp\u003eAs the results can be very large, output it modulo $$$m$$$.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line of the input gives the number of test cases, $$$T\\ (1 \\le T \\le 10)$$$. $$$T$$$ test cases follow.\u003c/p\u003e\u003cp\u003eFor each test case, the only line contains two integers $$$n\\ (1 \\le n \\le 3000)$$$ and $$$m\\ (1 \\le m \\le 10^9)$$$, where $$$n$$$ is the length of holy sequences and $$$m$$$ is the modulus.\u003c/p\u003e\u003cp\u003eThe sum of $$$n$$$ in all test cases doesn\u0027t exceed $$$10^4$$$.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eFor each test case, the output starts with a line containing \"\u003cspan class\u003d\"tex-font-style-tt\"\u003eCase #x:\u003c/span\u003e\", where $$$\\texttt{x}$$$ is the test case number (starting from $$$1$$$). The second line contains $$$n$$$ numbers, the answer for each $$$t \u003d 1,2,\\cdots, n$$$, modulo $$$m$$$.\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\n3 998\n10 998\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eCase #1:\n19 7 1\nCase #2:\n996 713 406 353 206 275 175 936 49 1\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}