Description:
This is an interactive problem. If you are unsure how interactive problems work, then it is recommended to read the guide for participants.
Before the last stage of the exam, the director conducted an interview. He gave Gon $$$n$$$ piles of stones, the $$$i$$$-th pile having $$$a_i$$$ stones.
Each stone is identical and weighs $$$1$$$ grams, except for one special stone that is part of an unknown pile and weighs $$$2$$$ grams.
A picture of the first test case. Pile $$$2$$$ has the special stone. The piles have weights of $$$1,3,3,4,5$$$, respectively.
Gon can only ask the director questions of one kind: he can choose $$$k$$$ piles, and the director will tell him the total weight of the piles chosen. More formally, Gon can choose an integer $$$k$$$ ($$$1 \leq k \leq n$$$) and $$$k$$$ unique piles $$$p_1, p_2, \dots, p_k$$$ ($$$1 \leq p_i \leq n$$$), and the director will return the total weight $$$m_{p_1} + m_{p_2} + \dots + m_{p_k}$$$, where $$$m_i$$$ denotes the weight of pile $$$i$$$.
Gon is tasked with finding the pile that contains the special stone. However, the director is busy. Help Gon find this pile in at most $$$\mathbf{30}$$$ queries.
Input Format:
The input data contains several test cases. The first line contains one integer $$$t$$$ ($$$1 \leq t \leq 1000$$$) — the number of test cases. The description of the test cases follows.
The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 2 \cdot 10^5$$$) — the number of piles.
The second line of each test case contains $$$n$$$ integers $$$a_i$$$ ($$$1 \leq a_i \leq 10^4$$$) — the number of stones in each pile.
It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.
After reading the input for each test case, proceed with the interaction as follows.
Output Format:
None
Note:
In the first test case, the stone with weight two is located in pile $$$2$$$, as shown in the picture. We perform the following interaction:
- $$$\texttt{? 4 1 2 3 4}$$$ — ask the total weight of piles $$$1$$$, $$$2$$$, $$$3$$$, and $$$4$$$. The total weight we receive back is $$$1+3+3+4=11$$$.
- $$$\texttt{? 2 2 3}$$$ — ask the total weight of piles $$$2$$$ and $$$3$$$. The total weight we receive back is $$$3+3=6$$$.
- $$$\texttt{? 1 2}$$$ — ask the total weight of pile $$$2$$$. The total weight we receive back is $$$3$$$.
- $$$\texttt{! 2}$$$ — we have figured out that pile $$$2$$$ contains the special stone, so we output it and move on to the next test case.
In the second test case, the stone with weight two is located on index $$$7$$$. We perform the following interaction:
- $$$\texttt{? 4 2 3 5 6}$$$ — ask the total weight of piles $$$2$$$, $$$3$$$, $$$5$$$, and $$$6$$$. The total weight we receive back is $$$2+3+3+4=12$$$.
- $$$\texttt{? 2 1 4}$$$ — ask the total weight of piles $$$1$$$ and $$$4$$$. The total weight we receive back is $$$1+5=6$$$.
- $$$\texttt{! 7}$$$ — we have somehow figured out that pile $$$7$$$ contains the special stone, so we output it and end the interaction.