P15711 [JAG 2023 Summer Camp #2] Tea time in the grand garden

Appropriate temperature changes are essential for brewing delicious tea. Noli has been taught a recipe for delicious tea. The recipe is represented by a sequence of non-negative integers $A = a_0, a_1, a_2, \ldots, a_N, a_{N+1}$ of length $N+2$. She must change the temperature accordingly. Raising the temperature is hard work. The cost of a recipe $A$ is defined by the following $f(A)$. $$ f(A) = \sum_{i=0}^{N} \max(0, a_{i+1} - a_i) $$ Noli has forgotten the recipe she was taught. All she remembers is that $a_0 = a_{N+1} = 0$ and that the cost was $K$. How many possible recipes can be considered? Find the remainder of the number of possible recipes divided by $998244353$. Note that two recipes are different when the values of $a_i$ are different for any $i (0 \leq i \leq N+1)$.

$N \ K$ The input satisfies the following constraints. - All inputs consist of integers. - $1 \leq N \leq 2 \times 10^5$ - $0 \leq K \leq 2 \times 10^5$

Output the remainder of the number of possible recipes divided by $998244353$. Add a new line at the end of the output.

In Sample Input 1, There are five possible sequences $A$. - $\{0,2,0,0\}$ - $\{0,0,2,0\}$ - $\{0,1,2,0\}$ - $\{0,2,1,0\}$ - $\{0,2,2,0\}$