There are $$$n+1$$$ people playing a game with dice. Every person has a dice of $$$m$$$ faces, each of which is equal-probability. Don't spend time wondering how this kind of dice can exist–You can image a generator which can generate numbers among $$$[1,m]$$$ with equal-probability.

At the beginning, each person throws his own dice, and the person with the smallest number of points loses. If more than one person throws the smallest number of dice at the same time, those who have thrown the smallest number of dice continue to throw dice until finally one person loses.

Walk Alone doesn't like randomness. He uses magic to fix the points the first person throws every time. That is, the first person will always throw $$$x$$$ points when the first person throws his dice, where $$$x$$$ is pre-chosen by Walk Alone, while other $$$n$$$ people still throw their dices randomly.

Now Walk Alone wants to know for every $$$x \in [1, m]$$$, the probability the first person will lose.

To be more precise, you need to output the probability modulo $$$998\ 244\ 353$$$. It can be proven that the probability can be presented as a fraction $$$\frac{p}{q}$$$. You need to output $$$p\cdot q^{998\ 244\ 351} \bmod 998\ 244\ 353$$$.