A14884. Star MST

In this problem, we will consider complete undirected graphs consisting of $n$ vertices with weighted edges. The weight of each edge is an integer from $1$ to $k$ .

An undirected graph is considered beautiful if the sum of weights of all edges incident to vertex $1$ is equal to the weight of MST in the graph. MST is the minimum spanning tree — a tree consisting of $n-1$ edges of the graph, which connects all $n$ vertices and has the minimum sum of weights among all such trees; the weight of MST is the sum of weights of all edges in it.

Calculate the number of complete beautiful graphs having exactly $n$ vertices and the weights of edges from $1$ to $k$ . Since the answer might be large, print it modulo $998244353$ .

The only line contains two integers $n$ and $k$ ( $2 \le n \le 250$ ; $1 \le k \le 250$ ).

Print one integer — the number of complete beautiful graphs having exactly $n$ vertices and the weights of edges from $1$ to $k$ . Since the answer might be large, print it modulo $998244353$ .