Blind Box

You are the owner of a store.

The store has launched a new blind box campaign. Each blind box contains $n$ cards, and there is a positive integer written on each card. The cards in each box are ordered so that the number on the $i$-th card is greater than or equal to the number on the $(i{-}1)$-th card for every $i > 1$. The integer on each card does not exceed $m$.

The store has all possible blind boxes satisfying these conditions, and no two boxes in the store are the same. Two boxes are different if and only if there is an index $i$ such that the numbers on the $i$-th cards of the two boxes differ.

You sell blind boxes at a fixed price. After a customer buys and opens a box, they ask you for a cashback equal to the product of the numbers on the $n$ cards in the box. Find the minimum price of each blind box such that your net income is non-negative after all boxes are sold.

The first line contains two integers $n$ and $m$: the number of cards in each box and the maximum value on a card ($1 \leq n, m \leq 10^5$).

Print a single integer: the minimum price, modulo $998\,244\,353$. The price may be a fraction. If the minimum price is the irreducible fraction $\frac{x}{y}$, print $x \cdot y^{-1} \bmod 998\,244\,353$, where $y^{-1}$ is an integer such that $y \cdot y^{-1} \bmod 998\,244\,353 = 1$.

Explanation of the first example: There are three different blind boxes: $(1,1)$, $(1,2)$, and $(2,2)$. Their cashback amounts are $1$, $2$, and $4$. So the minimum price is $\frac{7}{3}$.

The answer to the second example is $\frac{42525}{126} = \frac{675}{2}$.