AT_abc445_e [ABC445E] Many LCMs

You are given a sequence of positive integers $ A=(A_1,A_2,\dots,A_N) $ of length $ N $ . For each $ k=1,2,\dots,N $ , find the remainder when the least common multiple of the $ N-1 $ elements of $ A $ excluding $ A_k $ is divided by $ 998244353 $ . You are given $ T $ test cases; solve each of them.

The input is given from Standard Input in the following format: > $ T $ $ \mathrm{case}_1 $ $ \mathrm{case}_2 $ $ \vdots $ $ \mathrm{case}_T $ Here, $ \mathrm{case}_i $ denotes the input for the $ i $ -th test case. Each test case is given in the following format: > $ N $ $ A_1 $ $ A_2 $ $ \cdots $ $ A_N $

Output in the following format: > $ \mathrm{answer}_1 $ $ \mathrm{answer}_2 $ $ \vdots $ $ \mathrm{answer}_T $ Here, $ \mathrm{answer}_i $ denotes the output for the $ i $ -th test case. For each test case, output as follows. Let $ L_k $ be the remainder when the least common multiple of the $ N-1 $ elements of $ A $ excluding $ A_k $ is divided by $ 998244353 $ . Then, output in the following format: > $ L_1 $ $ L_2 $ $ \cdots $ $ L_N $

### Sample Explanation 1 For the first test case, the following holds. - The $ N-1 $ elements of $ A $ excluding $ A_1 $ are $ 12,25,8,15 $ , and their least common multiple is $ 600 $ . - The $ N-1 $ elements of $ A $ excluding $ A_2 $ are $ 9,25,8,15 $ , and their least common multiple is $ 1800 $ . - The $ N-1 $ elements of $ A $ excluding $ A_3 $ are $ 9,12,8,15 $ , and their least common multiple is $ 360 $ . - The $ N-1 $ elements of $ A $ excluding $ A_4 $ are $ 9,12,25,15 $ , and their least common multiple is $ 900 $ . - The $ N-1 $ elements of $ A $ excluding $ A_5 $ are $ 9,12,25,8 $ , and their least common multiple is $ 1800 $ . ### Constraints - $ 1 \leq T \leq 10^5 $ - $ 2 \leq N \leq 2 \times 10^5 $ - $ 1 \leq A_i \leq 10^7 $ - All input values are integers. - The sum of $ N $ over all test cases in a single input is at most $ 2 \times 10^5 $ .