Problem Statement

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 $998244353$.

Constraints

• $1\leq H,W$
• $HW\leq 2\times 10^5$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

H W

Output

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 $998244353$.