{"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\"\u003eLet $a_1, a_2$,... be an integer sequence beginning with $a_1$ \u003d 1. For n ≥ 1, $a_n$+1 is the sum of an and the sum of digits of $a_n$. That’s why we name the sequence a new Self-describing sequence.\u003cbr\u003eThe sequence starts with 1, 2, 4, 8, 16, 23, 28, 38, 49, ... and we also define the prefix sum $s_n \u003d a_1 + a_2 + ... + a_n$.\u003cbr\u003eFor given positive integer n, find $a_n$ and $s_n$.\u003cbr\u003e\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"The first line of input consists an integer T (T ≤ 32768), indicating the total number of test cases. Each of the following T lines provides an integer n (n ≤ 10^17).\u003cbr\u003e"}},{"title":"Output","value":{"format":"HTML","content":"For each test case output its case label first. Then for given n, output $a_n$ and $s_n$. Since the prefix sum is large,you only need to output $s_n$ mod 1000000009. However you should output $a_n$ as its exact value.\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\u003e7\r\n6\r\n66\r\n666\r\n6666\r\n66666\r\n123456789\r\n31415926535897932\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eCase #1: 23 54\r\nCase #2: 752 20862\r\nCase #3: 10949 3407733\r\nCase #4: 136193 441127485\r\nCase #5: 1698899 717710112\r\nCase #6: 5061289531 990040993\r\nCase #7: 2508156610654066874 660828136\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}