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 $1 \leq b < d \leq M$.

Input

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

Output

Print the answer in a single line.

Constraints

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

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

见题面 Input 部分

见题面 Output 部分