Problem Statement

We have a bar of length 1.
A point on the bar whose distance from the left end of the bar is x is said to have a coordinate x.
Snuke will do the operation below N times.

• Choose two real numbers x and y uniformly at random from [0, 1].
  Put a sticker covering the range from the coordinate $\min(x,y)$ to the coordinate $\max(x,y)$.

Here, all random choices are independent of each other.
Stickers can overlap.
The bar is said to be good when no point is covered by K+1 or more stickers.
Find the probability, modulo 998244353, of having a good bar after putting N stickers.
Definition of a probability modulo 998244353

It can be proved that the sought probability is always a rational number. Additionally, under the Constraints of this problem, when that value is represented as an irreducible fraction $\frac{P}{Q}$, it can be proved that $Q \not$ $\equiv 0 \pmod{998244353}.$ Thus, there is a unique integer R such that $R \times Q \equiv P \pmod{998244353}, 0 \leq R < 998244353.$ Report this R.

Input

Input is given from Standard Input in the following format:
N K

Output

Print the answer.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $1 \leq K \leq \min(N,10^5)$
• All values in input are integers.

Sample Input 1

2 1

Sample Output 1

332748118

We are to find the probability that the two stickers do not overlap, which is 1/3.

Sample Input 2

5 3

Sample Output 2

66549624

Sample Input 3

10000 5000

Sample Output 3

642557092

见题面 Input 部分

见题面 Output 部分