Problem Statement

You are given positive integers $N$ and $M$. Consider a weighted complete graph with $N$ vertices labeled from $1$ to $N$, where the weight of each edge is an integer between $1$ and $M$, inclusive. There are $M^{N(N-1)/2}$ such graphs. For each of them, consider the sum of the weights of the edges included in its Minimum Spanning Tree. What is the total of these sums? Print the result modulo $998244353$.

Constraints

• $2 \le N \le 500$
• $1 \le M \le 500$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N M

Output

Print the answer.