Background

The problem setter is too weak and can only make this kind of problem. It is slightly time-limit tight.

Problem Description

DLS likes climbing trees.
However, he does not want to put a data structure problem onto a tree; he likes counting Tree.

One day, he wants to build a tree by himself. He has $N$ nodes, labeled from $1$ to $N$, and he will connect edges between them. We define two trees to be different if and only if there exists a pair of nodes such that they are connected by an edge in one tree, but not connected by an edge in the other tree.
But he does not like a tree with too many branches, so he wants the maximum degree among all nodes in this tree to be $M$.

Since DLS is not very good at math and science, he hopes you can help him compute how many such trees there are.
Output the answer modulo $998244353$.

Input Format

A single line with two integers $N, M$.

Output Format

A single line with one integer, representing the answer.

3 2

3

7 4

2520

Hint

Translated by ChatGPT 5