Problem Statement

The following process is carried out on a permutation $P$ of $(1,2,\dots,N)$.

We have $N$ cards, numbered $1$ to $N$. Card $i$ has the integer $P_i$ written on it.

There are an integer $X=1$ and a boy called PCT, who initially has nothing. PCT does the following procedure for each $i=1,2,\dots,N$ in this order.

• Get Card $i$. Then, repeat the following action as long as he has a card with $X$ written on it:
• If PCT currently has $M$ or more cards, throw away all cards he has and terminate the process, without performing any more procedures.

Here, let us define the score of the permutation $P$ as follows:

• if the process is terminated by throwing away cards, the score of $P$ is $0$;
• if the process is carried out through the end without throwing away cards, the score of $P$ is $\prod_{i=1}^{N-1}$ $($ the number of cards PCT has at the end of the $i$-th procedure $)$.

There are $N!$ permutations $P$ of $(1,2,\dots,N)$. Find the sum of the scores of all those permutations, modulo $998244353$.

Constraints

• $2 \le N \le 2 \times 10^5$
• $2 \le M \le N$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M

Output

Print the answer.