{"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\"\u003eFor a positive integer $n$, let\u0027s denote function $f(n,m)$ as the $m$-th smallest integer $x$ that $x\u0026gt;n$ and $\\gcd(x,n)\u003d1$. For example, $f(5,1)\u003d6$ and $f(5,5)\u003d11$.\u003cbr\u003e\u003cbr\u003eYou are given the value of $m$ and $(f(n,m)-n)\\oplus n$, where ``$\\oplus$\u0027\u0027 denotes the bitwise XOR operation. Please write a program to find the smallest positive integer $n$ that $(f(n,m)-n)\\oplus n\u003dk$, or determine it is impossible.\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"The first line of the input contains an integer $T(1\\leq T\\leq 10)$, denoting the number of test cases.\u003cbr\u003e\u003cbr\u003eIn each test case, there are two integers $k,m(1\\leq k\\leq 10^{18},1\\leq m\\leq 100)$."}},{"title":"Output","value":{"format":"HTML","content":"For each test case, print a single line containing an integer, denoting the smallest $n$. If there is no solution, output ``$\\texttt{-1}$\u0027\u0027 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\u003e2\r\n3 5\r\n6 100\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e5\r\n-1\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}