{"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$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS-MML_HTMLorMML\" type\u003d\"text/javascript\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cdiv class\u003d\"panel_content\"\u003eMike has got a huge array $b$, and he is told that the array is encrypted.\u003cbr\u003e\u003cbr\u003eThe array is encrypted as follows.\u003cbr\u003e\u003cbr\u003eLet $a_i(0 \\leq i \u0026lt; n)$ be the $i$-th number of this original array.\u003cbr\u003e\u003cbr\u003eLet $b_i(0 \\leq i \u0026lt; n)$ be the $i$-th number of this encrypted array.\u003cbr\u003e\u003cbr\u003eLet $n$ be a power of $2$, which means $n \u003d 2^k$.\u003cbr\u003e\u003cbr\u003eThe $b_i$ is calculated as following.\u003cbr\u003e\u003cbr\u003e$$b_i \u003d \\sum_{0 \\leq j \u0026lt; n} f((i \\texttt{ or } j) \\texttt{ xor } i) a_j$$\u003cbr\u003e\u003cbr\u003e$f(x)$ means, if the number of $1$ in the binary of $x$ is even, it will return $1$, otherwise $0$.\u003cbr\u003e\u003cbr\u003eMike want to inverse the procedure of encryption.\u003cbr\u003e\u003cbr\u003ePlease help him recover the array $a$ with the array $b$.\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"The first line contains an integer $T$($T \\le 5$), denoting the number of the test cases.\u003cbr\u003e\u003cbr\u003eFor each test case, the first line contains an integer $k$($0 \\leq k \\leq 20$),\u003cbr\u003eThe next line contains $n \u003d 2^k$ integers, which are $b_i$ respectively.\u003cbr\u003e\u003cbr\u003eIt is guaranteed that, $a_i$ is an integer and $0 \\leq a_i \\leq 10^9$."}},{"title":"Output","value":{"format":"HTML","content":"For each test case, output \u0027\u0027Case #t:\u0027\u0027 to represent this is the t-th case. And then output the array $a$."}},{"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\n0\r\n233\r\n2\r\n5 3 4 10\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eCase #1: 233\r\nCase #2: 1 2 3 4\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}