问题 G: Competition

You participated in a competition and you have a number $V$ with an initial value of $0$ and a score $W$ with an initial value of $1$. When you win the game, firstly $V=V+2$, secondly $W=W\ast V$ ; when you lose the game, $V=V-1$.

Now you only know that you have won $n$ games and lost $m$ games.

Please find the sum of $W$ module $998244353$ for all possible situations.

Two situations are considered different if and only if the winning/losing sequences are different.

The first line contains two integers$n,m$.

2≤n≤5∗104, 1≤m≤105

5 5

133035