{"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\n\u003cscript\u003e\n window.katexOptions \u003d {\n delimiters: [\n {left: \u0027$$$$$$\u0027, right: \u0027$$$$$$\u0027, display: true},\n {left: \u0027$$$\u0027, right: \u0027$$$\u0027, display: false},\n {left: \u0027$$\u0027, right: \u0027$$\u0027, display: true},\n {left: \u0027$\u0027, right: \u0027$\u0027, display: false}\n ]\n };\n\u003c/script\u003e\n","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003e\u003cspan class\u003d\"tex-font-style-it\"\u003e\u003cspan class\u003d\"tex-font-style-bf\"\u003ePermutation\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ep\u003c/i\u003e\u003c/span\u003e is an ordered set of integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ep\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e, \u003ci\u003ep\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e, ..., \u003ci\u003ep\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e, consisting of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e distinct positive integers, each of them doesn\u0027t exceed \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e. We\u0027ll denote the \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e-th element of permutation \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ep\u003c/i\u003e\u003c/span\u003e as \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ep\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e. We\u0027ll call number \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e the size or the length of permutation \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ep\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e, \u003ci\u003ep\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e, ..., \u003ci\u003ep\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/p\u003e\u003cp\u003eWe\u0027ll call position \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003ei\u003c/i\u003e ≤ \u003ci\u003en\u003c/i\u003e\u003c/span\u003e) in permutation \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ep\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e, \u003ci\u003ep\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e, ..., \u003ci\u003ep\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e \u003cspan class\u003d\"tex-font-style-it\"\u003egood\u003c/span\u003e, if \u003cspan class\u003d\"tex-span\"\u003e|\u003ci\u003ep\u003c/i\u003e[\u003ci\u003ei\u003c/i\u003e] - \u003ci\u003ei\u003c/i\u003e| \u003d 1\u003c/span\u003e. Count the number of permutations of size \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e with exactly \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e good positions. Print the answer modulo \u003cspan class\u003d\"tex-span\"\u003e1000000007\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e10\u003csup class\u003d\"upper-index\"\u003e9\u003c/sup\u003e + 7\u003c/span\u003e).\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe single line 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\u003ek\u003c/i\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003en\u003c/i\u003e ≤ 1000, 0 ≤ \u003ci\u003ek\u003c/i\u003e ≤ \u003ci\u003en\u003c/i\u003e\u003c/span\u003e).\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003ePrint the number of permutations of length \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e with exactly \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e good positions modulo \u003cspan class\u003d\"tex-span\"\u003e1000000007\u003c/span\u003e (\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\u003e1 0\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1\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\u003e2 1\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e0\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 2\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e4\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\u003e4 1\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":"","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 4\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e328\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\u003eThe only permutation of size 1 has 0 good positions.\u003c/p\u003e\u003cp\u003ePermutation \u003cspan class\u003d\"tex-span\"\u003e(1, 2)\u003c/span\u003e has 0 good positions, and permutation \u003cspan class\u003d\"tex-span\"\u003e(2, 1)\u003c/span\u003e has 2 positions.\u003c/p\u003e\u003cp\u003ePermutations of size 3:\u003c/p\u003e\u003col\u003e\u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e(1, 2, 3)\u003c/span\u003e — 0 positions\u003c/li\u003e\u003cli\u003e \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/e06514fa06053090ed8361d0562e5c85?v\u003d1725716884\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e — 2 positions\u003c/li\u003e\u003cli\u003e \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/93dcf556164b8289c44fc4591820d708?v\u003d1725716884\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e — 2 positions\u003c/li\u003e\u003cli\u003e \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/70cab8732cfa18d0468736027f7a85a3?v\u003d1725716884\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e — 2 positions\u003c/li\u003e\u003cli\u003e \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/de93552b8e5de69ff6fec8a2a02ee9de?v\u003d1725716884\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e — 2 positions\u003c/li\u003e\u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e(3, 2, 1)\u003c/span\u003e — 0 positions\u003c/li\u003e\u003c/ol\u003e"}}]}