AT_arc199_d [ARC199D] Limestone

You are given positive integers $ H,W $ . There is an $ H \times W $ matrix $ A=(A_{i,j})\ (1\leq i\leq H,1\leq j\leq W) $ , where initially all elements are $ 0 $ . You can perform the following two types of operations on this matrix in any order and any number of times: - Choose integers $ r,c\ (1\leq r\leq H,1\leq c\leq W) $ . Set all of $ A_{r,1},A_{r,2},\ldots,A_{r,c} $ to $ 1 $ . - Choose integers $ r,c\ (1\leq r\leq H,1\leq c\leq W) $ . Set all of $ A_{1,c},A_{2,c},\ldots,A_{r,c} $ to $ 1 $ . Find the sum of $ \displaystyle \sum_{i=1}^H\sum_{j=1}^W A_{i,j} $ over all matrices that can be obtained by repeating the above operations, modulo $ 998244353 $ .

The input is given from Standard Input in the following format: > $ H $ $ W $

Output the sum of $ \displaystyle \sum_{i=1}^H\sum_{j=1}^W A_{i,j} $ over all matrices that can be obtained by repeating the operations, modulo $ 998244353 $ .

### Sample Explanation 1 There are $ 14 $ matrices that can be obtained by repeating the operations: $ \begin{pmatrix}0&0 \\ 0&0\end{pmatrix} \begin{pmatrix}1&0 \\ 0&0\end{pmatrix} \begin{pmatrix}0&1 \\ 0&0\end{pmatrix} \begin{pmatrix}1&1 \\ 0&0\end{pmatrix} \begin{pmatrix}0&0 \\ 1&0\end{pmatrix} \begin{pmatrix}1&0 \\ 1&0\end{pmatrix} \begin{pmatrix}0&1 \\ 1&0\end{pmatrix} \begin{pmatrix}1&1 \\ 1&0\end{pmatrix} \begin{pmatrix}0&1 \\ 0&1\end{pmatrix} \begin{pmatrix}1&1 \\ 0&1\end{pmatrix} \begin{pmatrix}0&0 \\ 1&1\end{pmatrix} \begin{pmatrix}1&0 \\ 1&1\end{pmatrix} \begin{pmatrix}0&1 \\ 1&1\end{pmatrix} \begin{pmatrix}1&1 \\ 1&1\end{pmatrix} $ The answer is $ 0+1+1+2+1+2+2+3+2+3+2+3+3+4=29 $ . $ \begin{pmatrix}0&0 \\ 0&1\end{pmatrix} $ and $ \begin{pmatrix}1&0 \\ 0&1\end{pmatrix} $ cannot be obtained by any sequence of operations. ### Constraints - $ 1\leq H,W $ - $ HW\leq 2\times 10^5 $ - All input values are integers.