{"trustable":false,"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":"Statement","value":{"format":"HTML","content":"\u003cp\u003e\nYou are working at a flower store which only sells red flowers and white flowers. You are designing a flower bouquet for a customer which can be represented as a sequence of several flowers, some of them white and some of them red.\n\u003c/p\u003e\n\n\u003cp\u003e\nBut, for a flower bouquet to be beautiful, there is a rule: The customer wants white flowers only in groups of size \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e.\n\u003c/p\u003e\n\n\u003cp\u003eIn how many ways You can design a flower bouquet of size between \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eb\u003c/i\u003e\u003c/span\u003e flowers. As the number of ways could be very large, print it 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\u003eInput contains several test cases.\u003c/p\u003e\n\n\u003cp\u003eThe first line contains two integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003et\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\u003et\u003c/i\u003e, \u003ci\u003ek\u003c/i\u003e ≤ 10\u003csup class\u003d\"upper-index\"\u003e5\u003c/sup\u003e\u003c/span\u003e), where \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003et\u003c/i\u003e\u003c/span\u003e represents the number of test cases.\u003c/p\u003e\n\n\u003cp\u003eThe next \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003et\u003c/i\u003e\u003c/span\u003e lines contain two integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eb\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\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e ≤ \u003ci\u003eb\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e ≤ 10\u003csup class\u003d\"upper-index\"\u003e5\u003c/sup\u003e\u003c/span\u003e), describing the \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e-th test.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003ePrint \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003et\u003c/i\u003e\u003c/span\u003e lines to the standard output. The \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e-th line should contain the number of ways in which You can design a flower bouquet of size between \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eb\u003c/i\u003e\u003c/span\u003e flowers 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":"Sample 1","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\n1 3\n2 3\n4 4\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e6\n5\n5\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":"\u003cul\u003e\n\u003cli\u003e\nFor \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eK\u003c/i\u003e\u003c/span\u003e \u003d \u003cspan class\u003d\"tex-span\"\u003e2\u003c/span\u003e and length \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e You can design (\u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eR\u003c/i\u003e\u003c/span\u003e).\n\u003c/li\u003e\n\u003cli\u003e\nFor \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eK\u003c/i\u003e\u003c/span\u003e \u003d \u003cspan class\u003d\"tex-span\"\u003e2\u003c/span\u003e and length \u003cspan class\u003d\"tex-span\"\u003e2\u003c/span\u003e You can design (\u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eRR\u003c/i\u003e\u003c/span\u003e) and (\u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eWW\u003c/i\u003e\u003c/span\u003e) (here the white flowers are in a group of 2).\n\u003c/li\u003e\n\u003cli\u003e\nFor \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eK\u003c/i\u003e\u003c/span\u003e \u003d \u003cspan class\u003d\"tex-span\"\u003e2\u003c/span\u003e and length \u003cspan class\u003d\"tex-span\"\u003e3\u003c/span\u003e You can design (\u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eRRR\u003c/i\u003e\u003c/span\u003e), (\u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eRWW\u003c/i\u003e\u003c/span\u003e) and (\u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eWWR\u003c/i\u003e\u003c/span\u003e).\n\u003c/li\u003e\n\u003cli\u003e\nFor \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eK\u003c/i\u003e\u003c/span\u003e \u003d \u003cspan class\u003d\"tex-span\"\u003e2\u003c/span\u003e and length \u003cspan class\u003d\"tex-span\"\u003e4\u003c/span\u003e You can design, for example, (\u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eWWWW\u003c/i\u003e\u003c/span\u003e) (here the white flowers are in groups of 2) or (\u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eRWWR\u003c/i\u003e\u003c/span\u003e), but for example You can\u0027t design (\u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eWWWR\u003c/i\u003e\u003c/span\u003e).\n\u003c/li\u003e\n\u003c/ul\u003e"}}]}