P5219 Boring Easy Problem I.

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

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 $998244353$.

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

A single line with one integer, representing the answer.

|Percentage of testdata|Constraints| |-|-| |$10\%$|$N, M \le 8$| |$30\%$|$N, M \le 100$| |$50\%$|$N, M \le 500$| |$70\%$|$N, M \le 2000$| |$100\%$|$2 \le N, M \le 5 \times 10^4$| Translated by ChatGPT 5