{"trustable":true,"prependHtml":"\u003cstyle type\u003d\"text/css\"\u003e\n section pre {\n display: block;\n padding: 9.5px;\n margin: 0 0 10px;\n font-size: 13px;\n line-height: 1.42857143;\n word-break: break-all;\n word-wrap: break-word;\n color: #333;\n background: rgba(255, 255, 255, 0.5);\n border: 1px solid #ccc;\n border-radius: 6px;\n }\n\u003c/style\u003e\n\u003cscript\u003e\n window.katexOptions \u003d {\n delimiters: [\n {left: \u0027\\\\(\u0027, right: \u0027\\\\)\u0027, display: false},\n {left: \u0027\\\\[\u0027, right: \u0027\\\\]\u0027, display: true}\n ]\n };\n\u003c/script\u003e\n","sections":[{"title":"Problem Statement","value":{"format":"HTML","content":"\r\n\u003csection\u003e\r\n\u003cp\u003eThere are \u003cvar\u003e\\(N\\)\u003c/var\u003e squares arranged in a row.\r\nThe squares are numbered \u003cvar\u003e\\(1\\)\u003c/var\u003e, \u003cvar\u003e\\(2\\)\u003c/var\u003e, \u003cvar\u003e\\(...\\)\u003c/var\u003e, \u003cvar\u003e\\(N\\)\u003c/var\u003e, from left to right.\u003c/p\u003e\r\n\u003cp\u003eSnuke is painting each square in red, green or blue.\r\nAccording to his aesthetic sense, the following \u003cvar\u003e\\(M\\)\u003c/var\u003e conditions must all be satisfied.\r\nThe \u003cvar\u003e\\(i\\)\u003c/var\u003e-th condition is:\u003c/p\u003e\r\n\u003cul\u003e\r\n\u003cli\u003eThere are exactly \u003cvar\u003e\\(x_i\\)\u003c/var\u003e different colors among squares \u003cvar\u003e\\(l_i\\)\u003c/var\u003e, \u003cvar\u003e\\(l_i + 1\\)\u003c/var\u003e, \u003cvar\u003e\\(...\\)\u003c/var\u003e, \u003cvar\u003e\\(r_i\\)\u003c/var\u003e.\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\u003cp\u003eIn how many ways can the squares be painted to satisfy all the conditions?\r\nFind the count modulo \u003cvar\u003e\\(10^9+7\\)\u003c/var\u003e.\u003c/p\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Constraints","value":{"format":"HTML","content":"\r\n\u003csection\u003e\r\n\u003cul\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(1 ≤ N ≤ 300\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(1 ≤ M ≤ 300\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(1 ≤ l_i ≤ r_i ≤ N\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(1 ≤ x_i ≤ 3\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Input","value":{"format":"HTML","content":"\r\n\u003csection\u003e\r\n\u003cp\u003eInput is given from Standard Input in the following format:\u003c/p\u003e\r\n\u003cpre\u003e\u003cvar\u003e\\(N\\)\u003c/var\u003e \u003cvar\u003e\\(M\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(l_1\\)\u003c/var\u003e \u003cvar\u003e\\(r_1\\)\u003c/var\u003e \u003cvar\u003e\\(x_1\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(l_2\\)\u003c/var\u003e \u003cvar\u003e\\(r_2\\)\u003c/var\u003e \u003cvar\u003e\\(x_2\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(:\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(l_M\\)\u003c/var\u003e \u003cvar\u003e\\(r_M\\)\u003c/var\u003e \u003cvar\u003e\\(x_M\\)\u003c/var\u003e\r\n\u003c/pre\u003e\r\n\r\n\u003c/section\u003e\r\n"}},{"title":"Output","value":{"format":"HTML","content":"\r\n\u003csection\u003e\r\n\u003cp\u003ePrint the number of ways to paint the squares to satisfy all the conditions, modulo \u003cvar\u003e\\(10^9+7\\)\u003c/var\u003e.\u003c/p\u003e\r\n\u003c/section\u003e\r\n"}},{"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 1\r\n1 3 3\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e6\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\r\n\u003csection\u003e\r\n\r\n\r\n\u003c/section\u003e\r\n\r\n\u003csection\u003e\r\n\r\n\r\n\u003cp\u003eThe six ways are:\u003c/p\u003e\r\n\u003cul\u003e\r\n\u003cli\u003eRGB\u003c/li\u003e\r\n\u003cli\u003eRBG\u003c/li\u003e\r\n\u003cli\u003eGRB\u003c/li\u003e\r\n\u003cli\u003eGBR\u003c/li\u003e\r\n\u003cli\u003eBRG\u003c/li\u003e\r\n\u003cli\u003eBGR\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\u003cp\u003ewhere R, G and B correspond to red, green and blue squares, respectively.\u003c/p\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Sample 2","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\r\n1 3 1\r\n2 4 2\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e6\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\r\n\u003csection\u003e\r\n\r\n\r\n\u003c/section\u003e\r\n\r\n\u003csection\u003e\r\n\r\n\r\n\u003cp\u003eThe six ways are:\u003c/p\u003e\r\n\u003cul\u003e\r\n\u003cli\u003eRRRG\u003c/li\u003e\r\n\u003cli\u003eRRRB\u003c/li\u003e\r\n\u003cli\u003eGGGR\u003c/li\u003e\r\n\u003cli\u003eGGGB\u003c/li\u003e\r\n\u003cli\u003eBBBR\u003c/li\u003e\r\n\u003cli\u003eBBBG\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Sample 3","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 3\r\n1 1 1\r\n1 1 2\r\n1 1 3\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e0\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\r\n\u003csection\u003e\r\n\r\n\r\n\u003c/section\u003e\r\n\r\n\u003csection\u003e\r\n\r\n\r\n\u003cp\u003eThere are zero ways.\u003c/p\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Sample 4","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\u003e8 10\r\n2 6 2\r\n5 5 1\r\n3 5 2\r\n4 7 3\r\n4 4 1\r\n2 3 1\r\n7 7 1\r\n1 5 2\r\n1 7 3\r\n3 4 2\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e108\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\r\n\u003csection\u003e\r\n\r\n\r\n\u003c/section\u003e\r\n\r\n\u003csection\u003e\r\n\u003c/section\u003e\r\n"}}]}