CF1799A Recent Actions

On Codeforces the "Recent Actions" field shows the last $ n $ posts with recent actions. Initially, there are posts $ 1, 2, \ldots, n $ in the field (this is in order from top to down). Also there are infinitely many posts not in the field, numbered with integers $ n + 1, n + 2, \ldots $ . When recent action happens in the post $ p $ : - If it is in the "Recent Actions" field, it moves from its position to the top position. - Otherwise, it is added to the top position, and the post on the down position is removed from the "Recent Actions" field. You know, that the next $ m $ recent actions will happen in the posts $ p_1, p_2, \ldots, p_m $ ( $ n + 1 \leq p_i \leq n + m $ ) in the moments of time $ 1, 2, \ldots, m $ . Note, that recent actions only happen with posts with numbers $ \geq n + 1 $ . For each post $ i $ ( $ 1 \leq i \leq n $ ), find the first time it will be removed from the "Recent Actions" field or say, that it won't be removed.

The first line contains a single integer $ t $ ( $ 1 \leq t \leq 10^4 $ ) — the number of test cases. Descriptions of test cases follow. The first line of each test case contains two integers $ n $ , $ m $ ( $ 1 \leq n, m \leq 5 \cdot 10^4 $ ) — the size of the "Recent Actions" field and the number of actions. The next line contains $ m $ integers $ p_1, p_2, \ldots, p_m $ ( $ n + 1 \leq p_i \leq n + m $ ). It is guaranteed, that the sum of $ n $ and the sum of $ m $ for all test cases does not exceed $ 5 \cdot 10^4 $ .

For each test case print $ n $ integers $ t_1, t_2, \ldots, t_n $ , where $ t_i=-1 $ if the post $ i $ won't be removed or $ t_i $ equals to the first moment of time the post $ i $ will be removed ( $ 1 \leq t_i \leq m $ ).

In the first test case, the only post $ 1 $ will be removed at the moment $ 1 $ and replaced by the post $ 2 $ . In the second test case the "Recent Actions" field will be (given an order from top to down): 1. Before moment $ 1 $ : $ [1, 2, 3] $ , after moment $ 1 $ : $ [5, 1, 2] $ . Post number $ 3 $ was removed. 2. Before moment $ 2 $ : $ [5, 1, 2] $ , after moment $ 2 $ : $ [4, 5, 1] $ . Post number $ 2 $ was removed. Post number $ 1 $ won't be removed. In the third test case the "Recent Actions" field will be (given an order from top to down): 1. Before moment $ 1 $ : $ [1, 2, 3, 4] $ , after moment $ 1 $ : $ [5, 1, 2, 3] $ . Post number $ 4 $ was removed. 2. Before moment $ 2 $ : $ [5, 1, 2, 3] $ , after moment $ 2 $ : $ [9, 5, 1, 2] $ . Post number $ 3 $ was removed. 3. Before moment $ 3 $ : $ [9, 5, 1, 2] $ , after moment $ 3 $ : $ [9, 5, 1, 2] $ . Nothing was changed. 4. Before moment $ 4 $ : $ [9, 5, 1, 2] $ , after moment $ 4 $ : $ [5, 9, 1, 2] $ . The order was changed. 5. Before moment $ 5 $ : $ [5, 9, 1, 2] $ , after moment $ 5 $ : $ [7, 5, 9, 1] $ . Post number $ 2 $ was removed. Post number $ 1 $ won't be removed.