CF1701D Permutation Restoration

Monocarp had a permutation $ a $ of $ n $ integers $ 1 $ , $ 2 $ , ..., $ n $ (a permutation is an array where each element from $ 1 $ to $ n $ occurs exactly once). Then Monocarp calculated an array of integers $ b $ of size $ n $ , where $ b_i = \left\lfloor \frac{i}{a_i} \right\rfloor $ . For example, if the permutation $ a $ is $ [2, 1, 4, 3] $ , then the array $ b $ is equal to $ \left[ \left\lfloor \frac{1}{2} \right\rfloor, \left\lfloor \frac{2}{1} \right\rfloor, \left\lfloor \frac{3}{4} \right\rfloor, \left\lfloor \frac{4}{3} \right\rfloor \right] = [0, 2, 0, 1] $ . Unfortunately, the Monocarp has lost his permutation, so he wants to restore it. Your task is to find a permutation $ a $ that corresponds to the given array $ b $ . If there are multiple possible permutations, then print any of them. The tests are constructed in such a way that least one suitable permutation exists.

The first line contains a single integer $ t $ ( $ 1 \le t \le 10^5 $ ) — number of test cases. The first line of each test case contains a single integer $ n $ ( $ 1 \le n \le 5 \cdot 10^5 $ ). The second line contains $ n $ integers $ b_1, b_2, \dots, b_n $ ( $ 0 \le b_i \le n $ ). Additional constrains on the input: - the sum of $ n $ over test cases does not exceed $ 5 \cdot 10^5 $ ; - there exists at least one permutation $ a $ that would yield this array $ b $ .

For each test case, print $ n $ integers — a permutation $ a $ that corresponds to the given array $ b $ . If there are multiple possible permutations, then print any of them.