E. Competition Graph
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Little A has obtained a competition graph.

Given $$$n,k$$$, find how many labeled competition graphs with $$$n$$$ vertices contain at least one $$$k$$$-cycle. The answer should be taken modulo $$$998244353$$$.

Please recall the following concepts with Little A:

Competition Graph: A directed graph with $$$n$$$ vertices and $$$\frac{n(n-1)}{2}$$$ edges, where there is exactly one directed edge between any two vertices with different labels.

$$$k$$$-cycle: A sequence of $$$k$$$ distinct vertices $$$v_1,v_2,\cdots,v_k$$$ such that there are directed edges in the graph: $$$$$$(v_1,v_2),(v_2,v_3),\cdots,(v_{k-1},v_k),(v_k,v_1)$$$$$$

Input

The first line contains two positive integers $$$n,k$$$ $$$(2 \leq n,k \leq 10^5)$$$.

Output

Output a single integer representing the answer, taken modulo $$$998244353$$$.

Examples
Input
3 2
Output
0
Input
3 3
Output
2