Problem Statement

There is a regular N-gon with side length D.
Starting from a vertex, we place black or white stones on the circumference at intervals of 1. As a result, each edge of the N-gon will have (D+1) stones on it, for a total of ND stones.
How many ways are there to place stones so that all edges have the same number of white stones on them? Find the count modulo 998244353.

Input

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

Output

Print the answer.

Constraints

• $3 \leq N \leq 10^{12}$
• $1 \leq D \leq 10^4$
• All values in input are integers.

Sample Input 1

3 2

Sample Output 1

10

There are 10 ways, as follows:

Sample Input 2

299792458 3141

Sample Output 2

138897974

Find the count modulo 998244353.

见题面 Input 部分

见题面 Output 部分