{"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\"\u003eNoticeļ¼Don\u0027t output extra spaces at the end of one line.\u003cbr\u003e\u003cbr\u003eDodo bird is jogging on an infinite 2-d plane, starting from $(x_0, y_0)$. For a point$(x, y)$, it is regarded as good if and only if $\\gcd(x,y)\u0026gt;1$.\u003cbr\u003e\u003cbr\u003eDodo bird will walk infinite steps on the plane under the following strategy:\u003cbr\u003e\u003cbr\u003eAssume he is currently at $(x, y)$, let $S$ be the set of good points among $(x-1,y-1),(x-1,y),(x-1,y+1),(x,y-1),(x,y+1),(x+1,y-1),(x+1,y),(x+1,y+1)$, $z$ be the size of $S$. He has a probability of $\\frac{1}{z+1}$ to stay in $(x, y)$, and he also has a probility of $\\frac{z}{z+1}$ to move to a point in $S$. If he chooses to move, the probility of going to any point in $S$ is equal.\u003cbr\u003e\u003cbr\u003eDefine $p_t$ as the probability of coming back to $(x_0, y_0)$ after walking $t$ steps, please calculate $\\lim_{t \\to \\infty}p_t$. It is guaranteed that the answer always exists.\u003cbr\u003e\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"The first line contains an integer $T(1 \\leq T \\leq 1000)$, indicating the number of test cases.\u003cbr\u003e\u003cbr\u003eEach test case has one line, which contains two integers $x, y(2 \\leq x_0, y_0 \\leq 10^{12})$, indicating the position of the start point. It is guaranteed that $\\gcd(x_0,y_0) \u0026gt; 1$.\u003cbr\u003e"}},{"title":"Output","value":{"format":"HTML","content":"$T$ lines, each line contains an irreducible fraction, indicating the answer. "}},{"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\u003e3\r\n18 16\r\n18 6\r\n18 8\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e0/1\r\n1/1\r\n2/7\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}