Star MST
Description
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 $998244353$.
Input
The only line contains two integers $n$ and $k$ ($2 \le n \le 250$; $1 \le k \le 250$).
Output
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 $998244353$.
Samples
3 2
5
4 4
571
6 9
310640163
42 13
136246935