Problem Statement

You are given positive integers $N$ and $M$. Among the $2^{NM}$ matrices $A$ with $N$ rows and $M$ columns where each element is $0$ or $1$, find the number, modulo $998244353$, of ones that satisfy the following condition:

• $A_{a, b} \\times A_{c, d} \\leq A_{a, d} \\times A_{c, b}$ for every quadruple of integers $(a, b, c, d)$ such that $1 \\leq a < c \\leq N$ and $1 \\leq b < d \\leq M$.

Constraints

• $1 \\leq N, M \\leq 400$
• All input values are integers.

Input

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

$N$ $M$

Output

Print the answer in a single line.

Sample Input 1

2 2

Sample Output 1

13

The condition is $A_{1,1} \\times A_{2,2} \\leq A_{1,2} \\times A_{2,1}$. All $13$ matrices other than $\\begin{pmatrix} 1 & 0 \\\\ 0 & 1 \\end{pmatrix}, \\begin{pmatrix} 1 & 1 \\\\ 0 & 1 \\end{pmatrix}, \\begin{pmatrix} 1 & 0 \\\\ 1 & 1 \\end{pmatrix}$ satisfy the condition.

Sample Input 2

1 30

Sample Output 2

75497471

All $2^{NM}$ matrices satisfy the condition, so print $2^{30}$ modulo $998244353$, that is, $75497471$.

Sample Input 3

400 400

Sample Output 3

412670892