{"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\u003eVasya has a set of \u003cspan class\u003d\"tex-span\"\u003e4\u003ci\u003en\u003c/i\u003e\u003c/span\u003e strings of equal length, consisting of lowercase English letters \"\u003cspan class\u003d\"tex-font-style-tt\"\u003ea\u003c/span\u003e\", \"\u003cspan class\u003d\"tex-font-style-tt\"\u003eb\u003c/span\u003e\", \"\u003cspan class\u003d\"tex-font-style-tt\"\u003ec\u003c/span\u003e\", \"\u003cspan class\u003d\"tex-font-style-tt\"\u003ed\u003c/span\u003e\" and \"\u003cspan class\u003d\"tex-font-style-tt\"\u003ee\u003c/span\u003e\". Moreover, the set is split into \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e groups of \u003cspan class\u003d\"tex-span\"\u003e4\u003c/span\u003e equal strings each. Vasya also has one special string \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003c/span\u003e of the same length, consisting of letters \"\u003cspan class\u003d\"tex-font-style-tt\"\u003ea\u003c/span\u003e\" only.\u003c/p\u003e\u003cp\u003eVasya wants to obtain from string \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003c/span\u003e some fixed string \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eb\u003c/i\u003e\u003c/span\u003e, in order to do this, he can use the strings from his set in any order. When he uses some string \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003c/span\u003e, each of the letters in string \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003c/span\u003e replaces with the next letter in alphabet as many times as the alphabet position, counting from zero, of the corresponding letter in string \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003c/span\u003e. Within this process the next letter in alphabet after \"\u003cspan class\u003d\"tex-font-style-tt\"\u003ee\u003c/span\u003e\" is \"\u003cspan class\u003d\"tex-font-style-tt\"\u003ea\u003c/span\u003e\".\u003c/p\u003e\u003cp\u003eFor example, if some letter in \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003c/span\u003e equals \"\u003cspan class\u003d\"tex-font-style-tt\"\u003eb\u003c/span\u003e\", and the letter on the same position in \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003c/span\u003e equals \"\u003cspan class\u003d\"tex-font-style-tt\"\u003ec\u003c/span\u003e\", then the letter in \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003c/span\u003e becomes equal \"\u003cspan class\u003d\"tex-font-style-tt\"\u003ed\u003c/span\u003e\", because \"\u003cspan class\u003d\"tex-font-style-tt\"\u003ec\u003c/span\u003e\" is the second alphabet letter, counting from zero. If some letter in \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003c/span\u003e equals \"\u003cspan class\u003d\"tex-font-style-tt\"\u003ee\u003c/span\u003e\", and on the same position in \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003c/span\u003e is \"\u003cspan class\u003d\"tex-font-style-tt\"\u003ed\u003c/span\u003e\", then the letter in \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003c/span\u003e becomes \"\u003cspan class\u003d\"tex-font-style-tt\"\u003ec\u003c/span\u003e\". For example, if the string \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003c/span\u003e equals \"\u003cspan class\u003d\"tex-font-style-tt\"\u003eabcde\u003c/span\u003e\", and string \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003c/span\u003e equals \"\u003cspan class\u003d\"tex-font-style-tt\"\u003ebaddc\u003c/span\u003e\", then \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003c/span\u003e becomes \"\u003cspan class\u003d\"tex-font-style-tt\"\u003ebbabb\u003c/span\u003e\".\u003c/p\u003e\u003cp\u003eA used string disappears, but Vasya can use equal strings several times.\u003c/p\u003e\u003cp\u003eVasya wants to know for \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eq\u003c/i\u003e\u003c/span\u003e given strings \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eb\u003c/i\u003e\u003c/span\u003e, how many ways there are to obtain from the string \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003c/span\u003e string \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eb\u003c/i\u003e\u003c/span\u003e using the given set of \u003cspan class\u003d\"tex-span\"\u003e4\u003ci\u003en\u003c/i\u003e\u003c/span\u003e strings? Two ways are different if the number of strings used from some group of \u003cspan class\u003d\"tex-span\"\u003e4\u003c/span\u003e strings is different. Help Vasya compute the answers for these questions modulo \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 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\u003em\u003c/i\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003en\u003c/i\u003e, \u003ci\u003em\u003c/i\u003e ≤ 500\u003c/span\u003e)\u0026nbsp;— the number of groups of four strings in the set, and the length of all strings.\u003c/p\u003e\u003cp\u003eEach of the next \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e lines contains a string \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003es\u003c/i\u003e\u003c/span\u003e of length \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e, consisting of lowercase English letters \"\u003cspan class\u003d\"tex-font-style-tt\"\u003ea\u003c/span\u003e\", \"\u003cspan class\u003d\"tex-font-style-tt\"\u003eb\u003c/span\u003e\", \"\u003cspan class\u003d\"tex-font-style-tt\"\u003ec\u003c/span\u003e\", \"\u003cspan class\u003d\"tex-font-style-tt\"\u003ed\u003c/span\u003e\" and \"\u003cspan class\u003d\"tex-font-style-tt\"\u003ee\u003c/span\u003e\". This means that there is a group of four strings equal to \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003es\u003c/i\u003e\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eThe next line contains single integer \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eq\u003c/i\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003eq\u003c/i\u003e ≤ 300\u003c/span\u003e)\u0026nbsp;— the number of strings \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eb\u003c/i\u003e\u003c/span\u003e Vasya is interested in.\u003c/p\u003e\u003cp\u003eEach of the next \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eq\u003c/i\u003e\u003c/span\u003e strings contains a string \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eb\u003c/i\u003e\u003c/span\u003e of length \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e, consisting of lowercase English letters \"\u003cspan class\u003d\"tex-font-style-tt\"\u003ea\u003c/span\u003e\", \"\u003cspan class\u003d\"tex-font-style-tt\"\u003eb\u003c/span\u003e\", \"\u003cspan class\u003d\"tex-font-style-tt\"\u003ec\u003c/span\u003e\", \"\u003cspan class\u003d\"tex-font-style-tt\"\u003ed\u003c/span\u003e\" and \"\u003cspan class\u003d\"tex-font-style-tt\"\u003ee\u003c/span\u003e\"\u0026nbsp;— a string Vasya is interested in.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eFor each string Vasya is interested in print the number of ways to obtain it from string \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003c/span\u003e, 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\u003e1 1\nb\n2\na\ne\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1\n1\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 4\naaaa\nbbbb\n1\ncccc\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e5\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\u003eIn the first example, we have \u003cspan class\u003d\"tex-span\"\u003e4\u003c/span\u003e strings \"\u003cspan class\u003d\"tex-font-style-tt\"\u003eb\u003c/span\u003e\". Then we have the only way for each string \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eb\u003c/i\u003e\u003c/span\u003e: select \u003cspan class\u003d\"tex-span\"\u003e0\u003c/span\u003e strings \"\u003cspan class\u003d\"tex-font-style-tt\"\u003eb\u003c/span\u003e\" to get \"\u003cspan class\u003d\"tex-font-style-tt\"\u003ea\u003c/span\u003e\" and select \u003cspan class\u003d\"tex-span\"\u003e4\u003c/span\u003e strings \"\u003cspan class\u003d\"tex-font-style-tt\"\u003eb\u003c/span\u003e\" to get \"\u003cspan class\u003d\"tex-font-style-tt\"\u003ee\u003c/span\u003e\", respectively. So, we have \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e way for each request.\u003c/p\u003e\u003cp\u003eIn the second example, note that the choice of the string \"\u003cspan class\u003d\"tex-font-style-tt\"\u003eaaaa\u003c/span\u003e\" does not change anything, that is we can choose any amount of it (from \u003cspan class\u003d\"tex-span\"\u003e0\u003c/span\u003e to \u003cspan class\u003d\"tex-span\"\u003e4\u003c/span\u003e, it\u0027s \u003cspan class\u003d\"tex-span\"\u003e5\u003c/span\u003e different ways) and we have to select the line \"\u003cspan class\u003d\"tex-font-style-tt\"\u003ebbbb\u003c/span\u003e\" \u003cspan class\u003d\"tex-span\"\u003e2\u003c/span\u003e times, since other variants do not fit. We get that we have \u003cspan class\u003d\"tex-span\"\u003e5\u003c/span\u003e ways for the request.\u003c/p\u003e"}}]}