{"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\u003eYou are given a set of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e elements indexed from \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e to \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e. The weight of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e-th element is \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ew\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e. The weight of some subset of a given set is denoted as \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/d8db2ce55b03f8bb491f900fcc794434?v\u003d1715487158\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e. The weight of some partition \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eR\u003c/i\u003e\u003c/span\u003e of a given set into \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e subsets is \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/6ef18bd21dababbbf7c3473d6788dcbd?v\u003d1715487158\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e (recall that a partition of a given set is a set of its subsets such that every element of the given set belongs to exactly one subset in partition).\u003c/p\u003e\u003cp\u003eCalculate the sum of weights of all partitions of a given set into exactly \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e \u003cspan class\u003d\"tex-font-style-bf\"\u003enon-empty\u003c/span\u003e subsets, and print it modulo \u003cspan class\u003d\"tex-span\"\u003e10\u003csup class\u003d\"upper-index\"\u003e9\u003c/sup\u003e + 7\u003c/span\u003e. Two partitions are considered different iff there exist two elements \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 such that they belong to the same set in one of the partitions, and to different sets in another partition.\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\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\u003ek\u003c/i\u003e ≤ \u003ci\u003en\u003c/i\u003e ≤ 2·10\u003csup class\u003d\"upper-index\"\u003e5\u003c/sup\u003e\u003c/span\u003e) — the number of elements and the number of subsets in each partition, respectively.\u003c/p\u003e\u003cp\u003eThe second line contains \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ew\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003ew\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e ≤ 10\u003csup class\u003d\"upper-index\"\u003e9\u003c/sup\u003e\u003c/span\u003e)— weights of elements of the set.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003ePrint one integer — the sum of weights of all partitions of a given set into \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e \u003cspan class\u003d\"tex-font-style-bf\"\u003enon-empty\u003c/span\u003e subsets, taken modulo \u003cspan class\u003d\"tex-span\"\u003e10\u003csup class\u003d\"upper-index\"\u003e9\u003c/sup\u003e + 7\u003c/span\u003e.\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\u003e4 2\n2 3 2 3\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e160\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 2\n1 2 3 4 5\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e645\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\u003ePossible partitions in the first sample:\u003c/p\u003e\u003col\u003e \u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e{{1, 2, 3}, {4}}\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eW\u003c/i\u003e(\u003ci\u003eR\u003c/i\u003e) \u003d 3·(\u003ci\u003ew\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e + \u003ci\u003ew\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e + \u003ci\u003ew\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e3\u003c/sub\u003e) + 1·\u003ci\u003ew\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e4\u003c/sub\u003e \u003d 24\u003c/span\u003e; \u003c/li\u003e\u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e{{1, 2, 4}, {3}}\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eW\u003c/i\u003e(\u003ci\u003eR\u003c/i\u003e) \u003d 26\u003c/span\u003e; \u003c/li\u003e\u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e{{1, 3, 4}, {2}}\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eW\u003c/i\u003e(\u003ci\u003eR\u003c/i\u003e) \u003d 24\u003c/span\u003e; \u003c/li\u003e\u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e{{1, 2}, {3, 4}}\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eW\u003c/i\u003e(\u003ci\u003eR\u003c/i\u003e) \u003d 2·(\u003ci\u003ew\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e + \u003ci\u003ew\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e) + 2·(\u003ci\u003ew\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e3\u003c/sub\u003e + \u003ci\u003ew\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e4\u003c/sub\u003e) \u003d 20\u003c/span\u003e; \u003c/li\u003e\u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e{{1, 3}, {2, 4}}\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eW\u003c/i\u003e(\u003ci\u003eR\u003c/i\u003e) \u003d 20\u003c/span\u003e; \u003c/li\u003e\u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e{{1, 4}, {2, 3}}\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eW\u003c/i\u003e(\u003ci\u003eR\u003c/i\u003e) \u003d 20\u003c/span\u003e; \u003c/li\u003e\u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e{{1}, {2, 3, 4}}\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eW\u003c/i\u003e(\u003ci\u003eR\u003c/i\u003e) \u003d 26\u003c/span\u003e; \u003c/li\u003e\u003c/ol\u003e\u003cp\u003ePossible partitions in the second sample:\u003c/p\u003e\u003col\u003e \u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e{{1, 2, 3, 4}, {5}}\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eW\u003c/i\u003e(\u003ci\u003eR\u003c/i\u003e) \u003d 45\u003c/span\u003e; \u003c/li\u003e\u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e{{1, 2, 3, 5}, {4}}\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eW\u003c/i\u003e(\u003ci\u003eR\u003c/i\u003e) \u003d 48\u003c/span\u003e; \u003c/li\u003e\u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e{{1, 2, 4, 5}, {3}}\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eW\u003c/i\u003e(\u003ci\u003eR\u003c/i\u003e) \u003d 51\u003c/span\u003e; \u003c/li\u003e\u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e{{1, 3, 4, 5}, {2}}\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eW\u003c/i\u003e(\u003ci\u003eR\u003c/i\u003e) \u003d 54\u003c/span\u003e; \u003c/li\u003e\u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e{{2, 3, 4, 5}, {1}}\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eW\u003c/i\u003e(\u003ci\u003eR\u003c/i\u003e) \u003d 57\u003c/span\u003e; \u003c/li\u003e\u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e{{1, 2, 3}, {4, 5}}\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eW\u003c/i\u003e(\u003ci\u003eR\u003c/i\u003e) \u003d 36\u003c/span\u003e; \u003c/li\u003e\u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e{{1, 2, 4}, {3, 5}}\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eW\u003c/i\u003e(\u003ci\u003eR\u003c/i\u003e) \u003d 37\u003c/span\u003e; \u003c/li\u003e\u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e{{1, 2, 5}, {3, 4}}\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eW\u003c/i\u003e(\u003ci\u003eR\u003c/i\u003e) \u003d 38\u003c/span\u003e; \u003c/li\u003e\u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e{{1, 3, 4}, {2, 5}}\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eW\u003c/i\u003e(\u003ci\u003eR\u003c/i\u003e) \u003d 38\u003c/span\u003e; \u003c/li\u003e\u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e{{1, 3, 5}, {2, 4}}\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eW\u003c/i\u003e(\u003ci\u003eR\u003c/i\u003e) \u003d 39\u003c/span\u003e; \u003c/li\u003e\u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e{{1, 4, 5}, {2, 3}}\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eW\u003c/i\u003e(\u003ci\u003eR\u003c/i\u003e) \u003d 40\u003c/span\u003e; \u003c/li\u003e\u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e{{2, 3, 4}, {1, 5}}\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eW\u003c/i\u003e(\u003ci\u003eR\u003c/i\u003e) \u003d 39\u003c/span\u003e; \u003c/li\u003e\u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e{{2, 3, 5}, {1, 4}}\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eW\u003c/i\u003e(\u003ci\u003eR\u003c/i\u003e) \u003d 40\u003c/span\u003e; \u003c/li\u003e\u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e{{2, 4, 5}, {1, 3}}\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eW\u003c/i\u003e(\u003ci\u003eR\u003c/i\u003e) \u003d 41\u003c/span\u003e; \u003c/li\u003e\u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e{{3, 4, 5}, {1, 2}}\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eW\u003c/i\u003e(\u003ci\u003eR\u003c/i\u003e) \u003d 42\u003c/span\u003e. \u003c/li\u003e\u003c/ol\u003e"}}]}