CF1582D Vupsen, Pupsen and 0

Vupsen and Pupsen were gifted an integer array. Since Vupsen doesn't like the number $ 0 $ , he threw away all numbers equal to $ 0 $ from the array. As a result, he got an array $ a $ of length $ n $ . Pupsen, on the contrary, likes the number $ 0 $ and he got upset when he saw the array without zeroes. To cheer Pupsen up, Vupsen decided to come up with another array $ b $ of length $ n $ such that $ \sum_{i=1}^{n}a_i \cdot b_i=0 $ . Since Vupsen doesn't like number $ 0 $ , the array $ b $ must not contain numbers equal to $ 0 $ . Also, the numbers in that array must not be huge, so the sum of their absolute values cannot exceed $ 10^9 $ . Please help Vupsen to find any such array $ b $ !

The first line contains a single integer $ t $ ( $ 1 \le t \le 100 $ ) — the number of test cases. The next $ 2 \cdot t $ lines contain the description of test cases. The description of each test case consists of two lines. The first line of each test case contains a single integer $ n $ ( $ 2 \le n \le 10^5 $ ) — the length of the array. The second line contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ -10^4 \le a_i \le 10^4 $ , $ a_i \neq 0 $ ) — the elements of the array $ a $ . It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2 \cdot 10^5 $ .

For each test case print $ n $ integers $ b_1, b_2, \ldots, b_n $ — elements of the array $ b $ ( $ |b_1|+|b_2|+\ldots +|b_n| \le 10^9 $ , $ b_i \neq 0 $ , $ \sum_{i=1}^{n}a_i \cdot b_i=0 $ ). It can be shown that the answer always exists.

In the first test case, $ 5 \cdot 1 + 5 \cdot (-1)=5-5=0 $ . You could also print $ 3 $ $ -3 $ , for example, since $ 5 \cdot 3 + 5 \cdot (-3)=15-15=0 $ In the second test case, $ 5 \cdot (-1) + (-2) \cdot 5 + 10 \cdot 1 + (-9) \cdot (-1) + 4 \cdot (-1)=-5-10+10+9-4=0 $ .