{"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\u003eWe have \u003cvar\u003e\\(N\\)\u003c/var\u003e bags.\u003cbr\u003e\r\nBag \u003cvar\u003e\\(i\\)\u003c/var\u003e contains \u003cvar\u003e\\(L_i\\)\u003c/var\u003e balls. The \u003cvar\u003e\\(j\\)\u003c/var\u003e-th ball \u003cvar\u003e\\((1\\leq j\\leq L_i)\\)\u003c/var\u003e in Bag \u003cvar\u003e\\(i\\)\u003c/var\u003e has a positive integer \u003cvar\u003e\\(a_{i,j}\\)\u003c/var\u003e written on it.\u003c/p\u003e\r\n\u003cp\u003eWe will pick out one ball from each bag.\u003cbr\u003e\r\nHow many ways are there to pick the balls so that the product of the numbers written on the picked balls is \u003cvar\u003e\\(X\\)\u003c/var\u003e?\u003c/p\u003e\r\n\u003cp\u003eHere, we distinguish all balls, even with the same numbers written on them.\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\\(N \\geq 2\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(L_i \\geq 2\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003eThe product of the numbers of balls in the bags is at most \u003cvar\u003e\\(10^5\\)\u003c/var\u003e: \u003cvar\u003e\\(\\displaystyle\\prod_{i\u003d1}^{N}L_i \\leq 10^5\\)\u003c/var\u003e.\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(1 \\leq a_{i,j} \\leq 10^9\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(1 \\leq X \\leq 10^{18}\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003eAll values in input are integers.\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\\(X\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(L_1\\)\u003c/var\u003e \u003cvar\u003e\\(a_{1,1}\\)\u003c/var\u003e \u003cvar\u003e\\(a_{1,2}\\)\u003c/var\u003e \u003cvar\u003e\\(\\ldots\\)\u003c/var\u003e \u003cvar\u003e\\(a_{1,L_1}\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(L_2\\)\u003c/var\u003e \u003cvar\u003e\\(a_{2,1}\\)\u003c/var\u003e \u003cvar\u003e\\(a_{2,2}\\)\u003c/var\u003e \u003cvar\u003e\\(\\ldots\\)\u003c/var\u003e \u003cvar\u003e\\(a_{2,L_2}\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(\\vdots\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(L_N\\)\u003c/var\u003e \u003cvar\u003e\\(a_{N,1}\\)\u003c/var\u003e \u003cvar\u003e\\(a_{N,2}\\)\u003c/var\u003e \u003cvar\u003e\\(\\ldots\\)\u003c/var\u003e \u003cvar\u003e\\(a_{N,L_N}\\)\u003c/var\u003e\r\n\u003c/pre\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Output","value":{"format":"HTML","content":"\r\n\u003csection\u003e\r\n\u003cp\u003ePrint the answer. \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\u003e2 40\r\n3 1 8 4\r\n2 10 5\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e2\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\u003c/section\u003e\r\n\r\n\u003csection\u003e\r\n\r\n\u003cp\u003eWhen choosing the \u003cvar\u003e\\(3\\)\u003c/var\u003e-rd ball in Bag \u003cvar\u003e\\(1\\)\u003c/var\u003e and \u003cvar\u003e\\(1\\)\u003c/var\u003e-st ball in Bag \u003cvar\u003e\\(2\\)\u003c/var\u003e, we have \u003cvar\u003e\\(a_{1,3} \\times a_{2,1} \u003d 4 \\times 10 \u003d 40\\)\u003c/var\u003e.\u003cbr\u003e\r\nWhen choosing the \u003cvar\u003e\\(2\\)\u003c/var\u003e-nd ball in Bag \u003cvar\u003e\\(1\\)\u003c/var\u003e and \u003cvar\u003e\\(2\\)\u003c/var\u003e-nd ball in Bag \u003cvar\u003e\\(2\\)\u003c/var\u003e, we have \u003cvar\u003e\\(a_{1,2} \\times a_{2,2} \u003d 8 \\times 5 \u003d 40\\)\u003c/var\u003e.\u003cbr\u003e\r\nThere are no other ways to make the product \u003cvar\u003e\\(40\\)\u003c/var\u003e, so the answer is \u003cvar\u003e\\(2\\)\u003c/var\u003e.\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\u003e3 200\r\n3 10 10 10\r\n3 10 10 10\r\n5 2 2 2 2 2\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e45\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\u003c/section\u003e\r\n\r\n\u003csection\u003e\r\n\r\n\u003cp\u003eNote that we distinguish all balls, even with the same numbers written on them.\u003c/p\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\u003e3 1000000000000000000\r\n2 1000000000 1000000000\r\n2 1000000000 1000000000\r\n2 1000000000 1000000000\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\u003c/section\u003e\r\n\r\n\u003csection\u003e\r\n\r\n\u003cp\u003eThere may be no way to make the product \u003cvar\u003e\\(X\\)\u003c/var\u003e.\u003c/p\u003e\u003c/section\u003e\r\n"}}]}