{"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\u003eA sequence of non-negative integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e, \u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e, ..., \u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e of length \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e is called a \u003cspan class\u003d\"tex-font-style-it\"\u003ewool sequence\u003c/span\u003e if and only if there exists two integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003el\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003er\u003c/i\u003e\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e(1 ≤ \u003ci\u003el\u003c/i\u003e ≤ \u003ci\u003er\u003c/i\u003e ≤ \u003ci\u003en\u003c/i\u003e)\u003c/span\u003e such that \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/a2f1333367b3d16f0a9450330446fbeb?v\u003d1715168717\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e. In other words each wool sequence contains a subsequence of consecutive elements with xor equal to 0.\u003c/p\u003e\u003cp\u003eThe expression \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/a184c15c2e05a72c66eb047c0fd89461?v\u003d1715168717\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e means applying the operation of a bitwise xor to numbers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ey\u003c/i\u003e\u003c/span\u003e. The given operation exists in all modern programming languages, for example, in languages \u003cspan class\u003d\"tex-font-style-it\"\u003eC++\u003c/span\u003e and \u003cspan class\u003d\"tex-font-style-it\"\u003eJava\u003c/span\u003e it is marked as \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e^\u003c/span\u003e\", in \u003cspan class\u003d\"tex-font-style-it\"\u003ePascal\u003c/span\u003e — as \"\u003cspan class\u003d\"tex-font-style-tt\"\u003exor\u003c/span\u003e\".\u003c/p\u003e\u003cp\u003eIn this problem you are asked to compute the number of sequences made of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e integers from 0 to \u003cspan class\u003d\"tex-span\"\u003e2\u003csup class\u003d\"upper-index\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/sup\u003e - 1\u003c/span\u003e that are not a wool sequence. You should print this number modulo \u003cspan class\u003d\"tex-span\"\u003e1000000009\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e(10\u003csup class\u003d\"upper-index\"\u003e9\u003c/sup\u003e + 9)\u003c/span\u003e.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe only line of input contains two space-separated integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e(1 ≤ \u003ci\u003en\u003c/i\u003e, \u003ci\u003em\u003c/i\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 the required number of sequences modulo \u003cspan class\u003d\"tex-span\"\u003e1000000009\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e(10\u003csup class\u003d\"upper-index\"\u003e9\u003c/sup\u003e + 9)\u003c/span\u003e on the only line of output.\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\u003e3 2\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e6\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\u003eSequences of length \u003cspan class\u003d\"tex-span\"\u003e3\u003c/span\u003e made of integers 0, 1, 2 and 3 that are not a wool sequence are \u003cspan class\u003d\"tex-font-style-tt\"\u003e(1, 3, 1)\u003c/span\u003e, \u003cspan class\u003d\"tex-font-style-tt\"\u003e(1, 2, 1)\u003c/span\u003e, \u003cspan class\u003d\"tex-font-style-tt\"\u003e(2, 1, 2)\u003c/span\u003e, \u003cspan class\u003d\"tex-font-style-tt\"\u003e(2, 3, 2)\u003c/span\u003e, \u003cspan class\u003d\"tex-font-style-tt\"\u003e(3, 1, 3)\u003c/span\u003e and \u003cspan class\u003d\"tex-font-style-tt\"\u003e(3, 2, 3)\u003c/span\u003e.\u003c/p\u003e"}}]}