{"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\"\u003eThere are \\(n\\) players passing ball on the football field.\u003cbr\u003e\u003cbr\u003eInitially, the first player has the ball. Then each second, the player with ball should pass the ball to any other player.\u003cbr\u003e\u003cbr\u003eAlice wonders how many way to pass the ball, such that after \\(t\\) seconds, the ball will turn back to the first player. So she asks Bob for help.\u003cbr\u003e\u003cbr\u003eNow, Bob solved the question and found that the answer modulo \\(998244353\\) is \\(x\\). But he forgot the exact number of \\(t\\). So he ask you for help, to find the smallest non-negative integer \\(t\\), such that the answer of Alice\u0027s question modulo \\(998244353\\) will be \\(x\\).\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"The first line contains an integer $T(1\\le T\\le 100)$representing the number of test cases.\u003cbr\u003e\u003cbr\u003eFor each test case, there are two integers $n,x(2\\le n\\le 10^{6}, 0\\le x \u0026lt; 998244353)$in one line."}},{"title":"Output","value":{"format":"HTML","content":"For each test case, output a single line containing one integer indicates the smallest $t$. If such $t$ do not exist, output \\(-1\\) instead. "}},{"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\u003e5\r\n11 1\r\n11 0\r\n11 10\r\n11 76805204\r\n11 2\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e0\r\n1\r\n2\r\n233333\r\n-1\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}