Codeforces Round 563 (Div. 2) |
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Finished |
This is an interactive problem.
You're given a tree consisting of n nodes, rooted at node 1. A tree is a connected graph with no cycles.
We chose a hidden node x. In order to find this node, you can ask queries of two types:
Node a is called an ancestor of node b if a≠b and the shortest path from node 1 to node b passes through node a. Note that in this problem a node is not an ancestor of itself.
Can you find x in no more than 36 queries? The hidden node is fixed in each test beforehand and does not depend on your queries.
The first line contains the integer n (2≤n≤2⋅105) — the number of nodes in the tree.
Each of the next n−1 lines contains two space-separated integers u and v (1≤u,v≤n) that mean there's an edge between nodes u and v. It's guaranteed that the given graph is a tree.
To print the answer, print "! x" (without quotes).
To ask a question, print it in one of the formats above:
After each question, you should read the answer: either the distance or the second vertex on the path, as mentioned in the legend.
If we answer with −1 instead of a valid answer, that means you exceeded the number of queries, made an invalid query, or violated the condition in the second type of queries. Exit immediately after receiving −1 and you will see Wrong answer verdict. Otherwise, you can get an arbitrary verdict because your solution will continue to read from a closed stream.
After printing a query, do not forget to output end of line and flush the output. Otherwise, you will get Idleness limit exceeded. To do this, use:
Hacks:
The first line should contain two integers n and x (2≤n≤2⋅105, 1≤x≤n).
Each of the next n−1 lines should contain two integers u and v (1≤u,v≤n) that mean there is an edge between nodes u and v. The edges must form a tree.
5 1 2 1 3 3 4 3 5 3 5
d 2 s 3 ! 5
In the first example, the hidden node is node 5.
We first ask about the distance between node x and node 2. The answer is 3, so node x is either 4 or 5. We then ask about the second node in the path from node 3 to node x. Note here that node 3 is an ancestor of node 5. We receive node 5 as the answer. Finally, we report that the hidden node is node 5.
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