AT_abc391_g [ABC391G] Many LCS

You are given a lowercase English string $ S $ of length $ N $ and an integer $ M $ . For each $ k=0,1,\ldots,N $ , solve the following problem: - There are $ 26^M $ lowercase English strings of length $ M $ . Among these, find the number, modulo $ 998244353 $ , of strings whose longest common subsequence with $ S $ has length exactly $ k $ .

The input is given from Standard Input in the following format: > $ N $ $ M $ $ S $

Let $ \mathrm{ans}_i $ be the answer for $ k=i $ . Print the answers in the following format: > $ \mathrm{ans}_0 $ $ \mathrm{ans}_1 $ $ \ldots $ $ \mathrm{ans}_N $

### Sample Explanation 1 The answers for $ k=0,1,2 $ are as follows: - For $ k=0 $ : Among length $ 2 $ lowercase English strings, those with a longest common subsequence of length $ 0 $ with `ab` include strings such as `cd`, `re`, `zz`, totaling $ 576 $ . - For $ k=1 $ : Among length $ 2 $ lowercase English strings, those with a longest common subsequence of length $ 1 $ with `ab` include strings such as `ac`, `wa`, `ba`, totaling $ 99 $ . - For $ k=2 $ : Among length $ 2 $ lowercase English strings, there is $ 1 $ string (`ab`) whose longest common subsequence with `ab` has length $ 2 $ . ### Constraints - $ 1\leq N\leq 10 $ - $ 1\leq M\leq 100 $ - $ N $ and $ M $ are integers. - $ S $ is a lowercase English string of length $ N $ .