AT_abc396_f [ABC396F] Rotated Inversions

You are given integers $ N, M $ and a length- $ N $ sequence of non-negative integers $ A = (A_1, A_2, \ldots, A_N) $ . For $ k = 0, 1, \ldots, M-1 $ , solve the following problem: > Define an integer sequence $ B = (B_1, B_2, \ldots, B_N) $ so that $ B_i $ is the remainder of $ A_i + k $ when divided by $ M $ . Find the inversion number in $ B $ . What is the inversion number? The inversion number of a sequence $ (A_1, A_2, \dots, A_N) $ is the number of integer pairs $ (i, j) $ satisfying $ 1 \le i < j \le N $ and $ A_i > A_j $ .

The input is given from Standard Input in the following format: > $ N $ $ M $ $ A_1 $ $ A_2 $ $ \ldots $ $ A_N $

Print $ M $ lines. The $ i $ -th line $ (1 \le i \le M) $ should contain the answer for the case $ k = i-1 $ .

### Sample Explanation 1 - For $ k=0 $ : $ B=(2, 1, 0) $ . The inversion number is $ 3 $ . - For $ k=1 $ : $ B=(0, 2, 1) $ . The inversion number is $ 1 $ . - For $ k=2 $ : $ B=(1, 0, 2) $ . The inversion number is $ 1 $ . ### Constraints - $ 1 \le N,M \le 2\times 10^5 $ - $ 0 \le A_i < M $ - All input values are integers.