30359번 - Tea time in the grand garden 다국어

문제

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 $A = a_0, a_1, a_2, \dots, a_N, a_{N+1}$ 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ドル$.

Note that two recipes are different when the values of $a_i$ are different for any $i$ (0ドル \le i \le N+1$).

입력

$N$ $K$

출력

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

제한

• All inputs consist of integers.
• 1ドル \le N \le 2 \times 10^5$
• 0ドル \le K \le 2 \times 10^5$

힌트

In Sample Input 1, There are five possible sequences $A$.

• $\{0,2,0,0\}$
• $\{0,0,2,0\}$
• $\{0,1,2,0\}$
• $\{0,2,1,0\}$
• $\{0,2,2,0\}$