CF2046B Move Back at a Cost

You are given an array of integers $ a $ of length $ n $ . You can perform the following operation zero or more times: - In one operation choose an index $ i $ ( $ 1 \le i \le n $ ), assign $ a_i := a_i + 1 $ , and then move $ a_i $ to the back of the array (to the rightmost position). For example, if $ a = [3, 5, 1, 9] $ , and you choose $ i = 2 $ , the array becomes $ [3, 1, 9, 6] $ . Find the lexicographically smallest $ ^{\text{∗}} $ array you can get by performing these operations. $ ^{\text{∗}} $ An array $ c $ is lexicographically smaller than an array $ d $ if and only if one of the following holds: - $ c $ is a prefix of $ d $ , but $ c \ne d $ ; or - in the first position where $ c $ and $ d $ differ, the array $ c $ has a smaller element than the corresponding element in $ d $ .

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 10^4 $ ). The description of the test cases follows. The first line contains a single integer $ n $ ( $ 1 \le n \le 10^5 $ ), the length of the array. The second line contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 1 \le a_i \le 10^9 $ ), the elements of the array. It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 10^5 $ .

For each test case, print the lexicographically smallest array you can get.