{"trustable":true,"prependHtml":"\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 async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS-MML_HTMLorMML\" type\u003d\"text/javascript\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cdiv class\u003d\"panel_content\"\u003e Teacher Mai finds that many problems about arithmetic function can be reduced to the following problem:\u003cbr\u003e\u003cbr\u003e Maintain an array a with index from 1 to l. There are two kinds of operations:\u003cbr\u003e\u003cbr\u003e\u0026nbsp;\u0026nbsp;1. Add v to a\u003csub\u003ex\u003c/sub\u003e for every x that gcd(x,n)\u003dd.\u003cbr\u003e\u0026nbsp;\u0026nbsp;2. Query \u003cimg style\u003d\"max-width:100%;\" src\u003d\"CDN_BASE_URL/e047b317857163f806fd043599c582cd?v\u003d1715986339\"\u003e \u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":" There are multiple test cases, terminated by a line \"0 0\".\u003cbr\u003e\u003cbr\u003e For each test case, the first line contains two integers l,Q(1\u0026lt;\u003dl,Q\u0026lt;\u003d5*10^4), indicating the length of the array and the number of the operations.\u003cbr\u003e\u003cbr\u003e In following Q lines, each line indicates an operation, and the format is \"1 n d v\" or \"2 x\" (1\u0026lt;\u003dn,d,v\u0026lt;\u003d2*10^5,1\u0026lt;\u003dx\u0026lt;\u003dl)."}},{"title":"Output","value":{"format":"HTML","content":" For each case, output \"Case #k:\" first, where k is the case number counting from 1.\u003cbr\u003e\u003cbr\u003e Then output the answer to each query."}},{"title":"Sample","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\u003e6 4\r\n1 4 1 2\r\n2 5\r\n1 3 3 3\r\n2 3\r\n0 0\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eCase #1:\r\n6\r\n7\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}