AT_abc416_d [ABC416D] Match, Mod, Minimize 2

You are given length- $ N $ sequences $ A=(A_1,A_2,\ldots,A_N) $ and $ B=(B_1,B_2,\ldots,B_N) $ consisting of non-negative integers, and a positive integer $ M $ . When you can freely rearrange the elements of $ A $ , find the minimum possible value of $ \displaystyle \sum_{i=1}^N \left((A_i+B_i) \bmod M\right) $ . $ T $ test cases are given, so find the answer for each of them.

The input is given from Standard Input in the following format: > $ T $ $ \text{case}_1 $ $ \text{case}_2 $ $ \vdots $ $ \text{case}_T $ Each test case $ \text{case}_i $ is given in the following format: > $ N $ $ M $ $ A_1 $ $ A_2 $ $ \ldots $ $ A_N $ $ B_1 $ $ B_2 $ $ \ldots $ $ B_N $

Output $ T $ lines. The $ j $ -th line should contain the minimum possible value of $ \displaystyle \sum_{i=1}^N \left((A_i+B_i) \bmod M\right) $ for the $ j $ -th test case.

### Sample Explanation 1 For the first test case, if we rearrange $ A $ as $ 4,3,1 $ , then $ (A_i+B_i)\bmod M $ becomes $ 0,3,2 $ , respectively, and their sum is $ 5 $ . ### Constraints - $ 1\le T \le 10^5 $ - $ 1\le N\le 3\times 10^5 $ - $ 1\le M\le 10^9 $ - $ 0\le A_i,B_i < M $ - The sum of $ N $ over all test cases is at most $ 3\times 10^5 $ . - All input values are integers.