CF1512D Corrupted Array

You are given a number $ n $ and an array $ b_1, b_2, \ldots, b_{n+2} $ , obtained according to the following algorithm: - some array $ a_1, a_2, \ldots, a_n $ was guessed; - array $ a $ was written to array $ b $ , i.e. $ b_i = a_i $ ( $ 1 \le i \le n $ ); - The $ (n+1) $ -th element of the array $ b $ is the sum of the numbers in the array $ a $ , i.e. $ b_{n+1} = a_1+a_2+\ldots+a_n $ ; - The $ (n+2) $ -th element of the array $ b $ was written some number $ x $ ( $ 1 \le x \le 10^9 $ ), i.e. $ b_{n+2} = x $ ; The - array $ b $ was shuffled. For example, the array $ b=[2, 3, 7, 12 ,2] $ it could be obtained in the following ways: - $ a=[2, 2, 3] $ and $ x=12 $ ; - $ a=[3, 2, 7] $ and $ x=2 $ . For the given array $ b $ , find any array $ a $ that could have been guessed initially.

The first line contains a single integer $ t $ ( $ 1 \le t \le 10^4 $ ). Then $ t $ test cases follow. The first line of each test case contains a single integer $ n $ ( $ 1 \le n \le 2 \cdot 10^5 $ ). The second row of each test case contains $ n+2 $ integers $ b_1, b_2, \ldots, b_{n+2} $ ( $ 1 \le b_i \le 10^9 $ ). It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2 \cdot 10^5 $ .

For each test case, output: - "-1", if the array $ b $ could not be obtained from any array $ a $ ; - $ n $ integers $ a_1, a_2, \ldots, a_n $ , otherwise. If there are several arrays of $ a $ , you can output any.