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:

• eat the card with X written on it, and then add 1 to X.

• 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.

Input

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

Output

Print the answer.

Constraints

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

Sample Input 1

3 2

Sample Output 1

1

For P=(3,1,2), the process goes as follows.

• The first procedure:
• PCT gets Card 1.

• PCT currently has 1 card, so he goes on.

• The second procedure:

• PCT gets Card 2.
• PCT eats Card 2 and make X = 2.

• PCT currently has 1 card, so he goes on.

• The third procedure:

• PCT gets Card 3.
• PCT eats Cards 1,3 and make X = 4.
• PCT currently has 0 cards, so he goes on.

The process is carried out through the end, so the score of (3,1,2) is $1 \times 1 = 1$.
Other than (3,1,2), there is no permutation with a score of 1 or greater, so the answer is 1.

Sample Input 2

3 3

Sample Output 2

5

Sample Input 3

146146 146

Sample Output 3

103537573

见题面 Input 部分

见题面 Output 部分