B'Note that the only difference between the easy and hard version is the constraint on the number of queries. You can make hacks only if all versions of the problem are solved. This is an interactive problem. You are given a tree consisting of n nodes numbered with integers from 1 to n . Ayush and Ashish chose two secret distinct nodes in the tree. You need to find out both the nodes. You can make the following query: Recall that a tree is a connected graph without cycles. The distance between two nodes is defined as the number of edges in the simple path between them. More formally, let 's define two hidden nodes as s and f . In one query you can provide the set of nodes {a_1, a_2, ldots, a_c } of the tree. As a result, you will get two numbers a_i and dist(a_i, s) + dist(a_i, f) . The node a_i is any node from the provided set, for which the number dist(a_i, s) + dist(a_i, f) is minimal. You can ask no more than 11 queries. The first line contains a single integer t (1 <= q t <= q 10) -- the number of test cases. Please note, how the interaction process is organized. The first line of each test case consists of a single integer n (2 <= n <= 1000) -- the number of nodes in the tree. The next n - 1 lines consist of two integers u , v (1 <= u, v <= n, u ne v) -- the edges of the tree. To ask a query print a single line: For each query, you will receive two integers x , d -- the node (among the queried nodes) with the minimum sum of distances to the hidden nodes and the sum of distances from that node to the hidden nodes. If the subset of nodes queried is invalid or you exceeded the number of queries then you will get x = d = -1 . In this case, you should terminate the program immediately. When you have guessed the hidden nodes, print a single line "! " (without quotes), followed by two integers in the range [1, n] '...