{"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\"\u003e\u0026nbsp;\u0026nbsp;Zero and One are good friends who always have fun with each other. This time, they decide to do something on a tree which is a kind of graph that there is only one path from node to node. First, Zero will give One an tree and every node in this tree has a value. Then, Zero will ask One a series of queries. Each query contains three parameters: x, y, z which mean that he want to know the maximum value produced by z xor each value on the path from node x to node y (include node x, node y). Unfortunately, One has no idea in this question. So he need you to solve it.\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u0026nbsp;\u0026nbsp;There are several test cases and the cases end with EOF. For each case:\u003cbr\u003e\u003cbr\u003e\u0026nbsp;\u0026nbsp;The first line contains two integers n(1\u0026lt;\u003dn\u0026lt;\u003d10^5) and m(1\u0026lt;\u003dm\u0026lt;\u003d10^5), which are the amount of tree’s nodes and queries, respectively.\u003cbr\u003e\u003cbr\u003e\u0026nbsp;\u0026nbsp;The second line contains n integers a[1..n] and a[i](0\u0026lt;\u003da[i]\u0026lt;2^{16}) is the value on the ith node.\u003cbr\u003e\u003cbr\u003e\u0026nbsp;\u0026nbsp;The next n–1 lines contains two integers u v, which means there is an connection between u and v.\u003cbr\u003e\u003cbr\u003e\u0026nbsp;\u0026nbsp;The next m lines contains three integers x y z, which are the parameters of Zero’s query.\u003cbr\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u0026nbsp;\u0026nbsp;For each query, output the answer.\u003cbr\u003e"}},{"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 2\r\n1 2 2\r\n1 2\r\n2 3\r\n1 3 1\r\n2 3 2\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e3\r\n0\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}