Star MST

6000ms

524288K

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 $$$998244353$$$.

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 $$$998244353$$$.

Sample Input:

3 2

Sample Output:

Sample Input:

4 4

Sample Output:

Sample Input:

6 9

Sample Output:

310640163

Sample Input:

42 13

Sample Output:

136246935

Informação

Provedor Codeforces

Código CF1657E