CF1657E.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 $998244353$.

本题中，我们考虑由 $n$ 个顶点构成的完全无向图，其每条边均带有整数权重，且权重取值范围为 $1$ 到 $k$（含端点）。

若一个无向图满足：与顶点 $1$ 相连的所有边的权重之和等于该图的最小生成树（MST）的权重，则称其为优美的图。
其中，最小生成树（MST）是指图中一棵包含全部 $n$ 个顶点、恰好由 $n-1$ 条边构成的树，且在所有满足此条件的树中，其所有边的权重之和最小；MST 的权重即为其所含所有边的权重之和。

请计算：恰好含有 $n$ 个顶点、且所有边的权重均取自 $1$ 至 $k$ 的完全优美图的个数。由于答案可能很大，请对 $998244353$ 取模后输出。

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

唯一一行包含两个整数 $n$ 和 $k$（$2 \le n \le 250$；$1 \le k \le 250$）。

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 $998244353$.

输出一个整数——恰好具有 $n$ 个顶点、且边权取自 $1$ 到 $k$ 的完全优美图的个数。由于答案可能很大，请对 $998244353$ 取模后输出。