B"Lech got into a tree consisting of n vertices with a root in vertex number 1. At each vertex i written integer ai. He will not get out until he answers q queries of the form u v. Answer for the query is maximal value among all vertices i on path from u to v including u and v, where dist(i, xe2 x80 x89v) is number of edges on path from i to v. Also guaranteed that vertex u is ancestor of vertex v. Leha's tastes are very singular: he believes that vertex is ancestor of itself. Help Leha to get out. The expression means the bitwise exclusive OR to the numbers x and y. Note that vertex u is ancestor of vertex v if vertex u lies on the path from root to the vertex v. First line of input data contains two integers n and q (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89n xe2 x80 x89 xe2 x89 xa4 xe2 x80 x895 xc2 xb7104, 1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89q xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89150 xe2 x80 x89000) -- number of vertices in the tree and number of queries respectively. Next line contains n integers a1, xe2 x80 x89a2, xe2 x80 x89..., xe2 x80 x89an (0 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89ai xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89n) -- numbers on vertices. Each of next n xe2 x80 x89- xe2 x80 x891 lines contains two integers u and v (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89u, xe2 x80 x89v xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89n) -- description of the edges in tree. Guaranteed that given graph is a tree. Each of next q lines contains two integers u and v (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89u, xe2 x80 x89v xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89n) -- description of queries. Guaranteed that vertex u is ancestor of vertex v. Output q lines -- answers for a queries. "...