E. Star MST
time limit per test
6 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

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 $998244353$.

Examples
Input
3 2

Output
5

Input
4 4

Output
571

Input
6 9

Output
310640163

Input
42 13

Output
136246935