C. Multiple?
time limit per test
4 seconds
memory limit per test
256 mebibytes
input
standard input
output
standard output

Given an integer $$$n$$$, the sequence is called good if its elements are from $$$[1, n]$$$ and all its non-empty subsequences (not necessarily continuous) have sums not divisible by $$$n$$$.

Calculate the number of good sequences of length $$$n-k$$$ modulo $$$998\,244\,353$$$.

Input

The only line of input contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le k \le n/4 \lt n \lt 998\,244\,353$$$).

Output

Print one number — the answer to the problem.

Examples
Input
4 1
Output
2
Input
9 2
Output
48
Input
222222222 222222
Output
851798824