{"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\"\u003eIn mathematics, the greatest common divisor (gcd), also known as the greatest common factor (gcf), highest common factor (hcf), or greatest common measure (gcm), of two or more integers (when at least one of them is not zero), is the largest positive integer that divides the numbers without a remainder.\u003cbr\u003e---Wikipedia\u003cbr\u003e\u003cbr\u003eToday, GCD takes revenge on you. You have to figure out the k-th GCD of X and Y.\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"The first line contains a single integer T, indicating the number of test cases. \u003cbr\u003e\u003cbr\u003eEach test case only contains three integers X, Y and K.\u003cbr\u003e\u003cbr\u003e[Technical Specification]\u003cbr\u003e1. 1 \u0026lt;\u003d T \u0026lt;\u003d 100\u003cbr\u003e2. 1 \u0026lt;\u003d X, Y, K \u0026lt;\u003d 1 000 000 000 000\u003cbr\u003e"}},{"title":"Output","value":{"format":"HTML","content":"For each test case, output the k-th GCD of X and Y. If no such integer exists, output -1."}},{"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\n2 3 1\r\n2 3 2\r\n8 16 3\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1\r\n-1\r\n2\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}