{"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\"\u003eAs we know, Rikka is poor at math. At the test, Rikka finds that she cannot even do a single problem. There is one of the insane problems:\u003cbr\u003e\u003cbr\u003eGiven an integer $K$, she needs to come up with an $n \\times n$ $01$ matrix $A$ and an integer $m$ which meet $B_{1,n}\u003dK$, where $B\u003dA^m$.\u003cbr\u003e\u003cbr\u003eIt is too difficult for Rikka. Can you help her?\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"The first line of the input is a single integer $T\\ (T\u003d40)$, indicating the number of testcases. \u003cbr\u003e\u003cbr\u003eEach of the next $T$ lines contains one integer $K\\ (0 \\leq K \\leq 10^{18})$. "}},{"title":"Output","value":{"format":"HTML","content":"For each testcase, the first line contains two space-separated integers $n,m\\ (1 \\leq n,m \\leq 30)$.\u003cbr\u003e\u003cbr\u003eIn each of following $n$ lines print $n$ characters (0 or 1) - the matrix $A$ you find."}},{"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\u003e1\r\n4\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e2 4\r\n11\r\n01\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}