Star MST

题意翻译

有一个 $n$ 个点的无向完全图，边权 $ e∈[1,k]$ ，已知该图的最小生成树的权值与所有与 $1$ 号点相连的边的边权和相同，求有多少种构图方式，答案对 $998244353$ 取模，$2\leq n \leq 250 , 1 \leq k \leq 250$ 。

题目描述

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 $ .

输入输出格式

输入格式

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

输出格式

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 $ .

输入输出样例

输入样例 #1

3 2

输出样例 #1

5

输入样例 #2

4 4

输出样例 #2

571

输入样例 #3

6 9

输出样例 #3

310640163

输入样例 #4

42 13

输出样例 #4

136246935