{"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\"\u003eLet $f(s)$ be a hash function of string $s$. If $s\u003ds_0s_1\\dots s_{n-1}$,$f(s)\u003d(\\sum_{i\u003d0}^{n-1} w(s_i)base^i) \\bmod r$.\u003cbr\u003e\u003cbr\u003eTeacher Mai wants to find two different regular bracket sequences $a,b$ with the same length$(\\leq 10^4)$ and the same hash value$(f(a)\u003df(b))$, where w(\"(\")\u003d$p$,w(\")\")\u003d$q$.\u003cbr\u003e\u003cbr\u003eLet us define a regular brackets sequence in the following way: Empty sequence is a regular sequence. If $S$ is a regular sequence, then $(S)$ is regular sequences. If $A$ and $B$ are regular sequences, then $AB$ is a regular sequence.\u003cbr\u003e\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"There are multiple test cases. All the test cases are generated randomly.\u003cbr\u003e\u003cbr\u003eFor each test case, there is one line contains four numbers $p,q,r,base(1\\leq p,q,r,base\\leq 10^{18})$\u003cbr\u003e"}},{"title":"Output","value":{"format":"HTML","content":"For each test case, print two different regular bracket sequences $a,b$ with the same length$(\\leq 10^4)$ and the same hash value$(f(a)\u003df(b))$"}},{"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\u003e4 7 37 10\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e((()))\r\n()()()\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}