This is a run-twice (communication) interactive problem. There are two players: Player A (Neri) and Player B (Mashiro). The jury will first interact with Player A. After Player A ends their interaction, the jury will interact with Player B. Note that Player A and Player B may not directly pass information to each other; both players are only able to send information to or receive information from the jury, but they may agree on the strategy they will use to communicate. Before the interaction, the jury determines an undirected tree (T) of size (n) and an integer (s) ((1\le s\le 2^{n-1})). These values are consistent across both players. Player A (Neri) first receives the two integers (n) and (s) from the jury without acquiring extra information about the tree (T). Then, the jury will interact with Neri for exactly (n-1) rounds. In each round of interaction: The jury will reveal an undirected edge of (T) to Neri, and then Neri needs to assign a direction to it immediately . Note that all (n-1) edges of (T) are directed after this interaction, forming a new directed tree (T'). Player B (Mashiro) receives the directed tree (T') created in the interaction between Neri and the jury. Her task is to determine the value of (s) according to the information she receives. Neri wants to ensure that Mashiro can determine the integer (s). Your task is to act as both players and determine an optimal interaction strategy for both players so that Mashiro can determine the integer (s) correctly. First Run Your code will be run exactly two times on each test. On the first run, you will be Player A (Neri). Input The first line of the input contains two integers (t) and (q) ((1 \le t \le 10^4), (q=1)) — the number of test cases and the run number. Here, the purpose of giving (q=1) is so your program recognizes that this is its first run, and it should act as Player A (Neri). For each test case,