Problem Description

Let $x = 40^{76^{93}}$. There are $n$ points on a plane, with the $i$-th point located at coordinates $(x^i, 0)$.

Perform $m$ operations, where each operation selects two points $A$ and $B$, rotates $A$ 60 degrees clockwise around $B$, and then removes $B$.

Determine the number of possible positions for the center of mass of the remaining points, modulo $998244353$.

Constraints: $2 \le n \le 407693$, $1 \le m \le n-1$.

Input Format

A single line containing two integers $n$ and $m$.

Output Format

A single line containing the answer modulo $998244353$.

Sample Input and Output

Sample Input #1

3 2

Sample Output #1

12

Sample Input #2

4 3

Sample Output #2

60

Sample Input #3

22 21

Sample Output #3

478037653

Sample Input #4

407693 333333

Sample Output #4

971291318

Notes

This problem consists of a single subtask, and you must pass all data points to receive points.

见题面 Input 部分

见题面 Output 部分