E. Star MSTtime limit per test6 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputIn 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.InputThe only line contains two integers n and k (2 \le n \le 250; 1 \le k \le 250).OutputPrint 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.ExamplesInput
3 2
Output
5
Input
4 4
Output
571
Input
6 9
Output
310640163
Input
42 13
Output
136246935

3 2

5 
['combinatorics', 'dp', 'graph matchings', 'math', '*2200']