Problem Statement

Consider the hexagon $ABCDEF$ on the $xy$-plane with vertices $A=(1,0),B=(a,0),C=(a,b-1),D=(a-1,b),E=(0,b),F=(0,1)$.

We tile this hexagon with the following $3$ types of shapes. Shape $1$ is a square with side length $1$, and shapes $2,3$ are parallelograms with two sides of lengths $1,\sqrt{2}$ where the angle between these two sides is $45^{\circ}$.

How many ways are there to tile the hexagon with these shapes, without rotating or reflecting them, so that there are no gaps or overlaps? Find the answer modulo $998244353$.

Constraints

• $2\le a,b\le 10^5$
• All inputs are integers.

Input

$a$ $b$

Output

Output the total number of tilings modulo $998244353$.

Sample

Sample 1

Input

2 3

Output

3

There are the following $3$ ways.

31415 92653

556511073