CF1942B Bessie and MEX

[MOOO! - Doja Cat](https://soundcloud.com/amalaofficial/mooo) ⠀ Farmer John has a permutation $ p_1, p_2, \ldots, p_n $ , where every integer from $ 0 $ to $ n-1 $ occurs exactly once. He gives Bessie an array $ a $ of length $ n $ and challenges her to construct $ p $ based on $ a $ . The array $ a $ is constructed so that $ a_i $ = $ \texttt{MEX}(p_1, p_2, \ldots, p_i) - p_i $ , where the $ \texttt{MEX} $ of an array is the minimum non-negative integer that does not appear in that array. For example, $ \texttt{MEX}(1, 2, 3) = 0 $ and $ \texttt{MEX}(3, 1, 0) = 2 $ . Help Bessie construct any valid permutation $ p $ that satisfies $ a $ . The input is given in such a way that at least one valid $ p $ exists. If there are multiple possible $ p $ , it is enough to print one of them.

The first line contains $ t $ ( $ 1 \leq t \leq 10^4 $ ) — the number of test cases. The first line of each test case contains an integer $ n $ ( $ 1 \leq n \leq 2 \cdot 10^5 $ ) — the lengths of $ p $ and $ a $ . The second line of each test case contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ -n \leq a_i \leq n $ ) — the elements of array $ a $ . It is guaranteed that there is at least one valid $ p $ for the given data. It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2 \cdot 10^5 $ .

For each test case, output $ n $ integers on a new line, the elements of $ p $ . If there are multiple solutions, print any of them.

In the first case, $ p = [0, 1, 4, 2, 3] $ is one possible output. $ a $ will then be calculated as $ a_1 = \texttt{MEX}(0) - 0 = 1 $ , $ a_2 = \texttt{MEX}(0, 1) - 1 = 1 $ , $ a_3 = \texttt{MEX}(0, 1, 4) - 4 = -2 $ , $ a_4 = \texttt{MEX}(0, 1, 4, 2) - 2 = 1 $ , $ a_5 = \texttt{MEX}(0, 1, 4, 2, 3) - 3 = 2 $ . So, as required, $ a $ will be $ [1, 1, -2, 1, 2] $ .