Problem9907--ABC309 —— G - Ban Permutation

9907: ABC309 —— G - Ban Permutation

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Time Limit : 1.000 sec  Memory Limit : 512 MiB

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Description

Find the number, modulo $998244353$, of permutations $P=(P_1,P_2,\dots,P_N)$ of $(1,2,\dots,N)$ such that:

-   $|P_i - i| \ge X$ for all integers $i$ with $1 \le i \le N$.

Input

The input is given from Standard Input in the following format:

```
$N$ $X$
```

Output

Print the answer.

Constraints

-   $1 \le N \le 100$
-   $1 \le X \le 5$
-   All input values are integers.

Sample 1 Input 

3 1

Sample 1 Output 

2
The conforming permutations P=(P1,P2,P3) are the following two, (2,3,1) and (3,1,2), so the answer is 2.

Sample 2 Input 

5 2

Sample 2 Output 

4

Sample 3 Input 

98 5

Sample 3 Output 

809422418

Source/Category

 
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