Score: $1000$ points

问题陈述

有一棵包含 $NM+1$ 个顶点的树，编号从 $0$ 到 $NM$。第 $i$ 条边（$1 \le i \le NM$）连接顶点 $i$ 和 $\max(i-N,0)$。

最初，顶点 $i$ 被涂成颜色 $i \bmod N$。你可以执行以下操作零次或多次：

• 选择两个由边连接的顶点 $u$ 和 $v$。将顶点 $u$ 的颜色重新涂成顶点 $v$ 的颜色。

在操作后，找出可能的树的数量，对 $998244353$ 取模。如果某个顶点的颜色不同，则区分两棵树。

以上为大语言模型 kimi 翻译，仅供参考。

Problem Statement

There is a tree with $NM+1$ vertices numbered $0$ to $NM$. The $i$-th edge ($1 \le i \le NM$) connects vertices $i$ and $\max(i-N,0)$.

Initially, vertex $i$ is colored with color $i \bmod N$. You can perform the following operation zero or more times:

• Choose two vertices $u$ and $v$ connected by an edge. Repaint the color of vertex $u$ with that of vertex $v$.

Find the number, modulo $998244353$, of possible trees after the operations. Two trees are distinguished if and only if some vertex has different colors.

Constraints

• $1 \le N, M \le 2 \times 10^5$

Input

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

$N$ $M$

Output

Print the answer.

Sample Input 1

3 1

Sample Output 1

42

One possible sequence of operations is as follows. Including this one, there are $42$ possible final trees.

Sample Input 2

4 2

Sample Output 2

219100

Sample Input 3

20 24

Sample Output 3

984288778

Sample Input 4

123456 112233

Sample Output 4

764098676