Score : $575$ points

问题描述

求满足以下条件的从 $(1,2,\dots,N)$ 到自身的排列 $P=(P_1,P_2,\dots,P_N)$ 的个数，模 $998244353$：

• 对于所有整数 $i$，满足 $1 \le i \le N$，均有 $|P_i - i| \ge X$。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

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 $1 \le i \le N$.

Constraints

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

Input

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

$N$ $X$

Output

Print the answer.

Sample Input 1

3 1

Sample Output 1

2

The conforming permutations $P=(P_1,P_2,P_3)$ are the following two, $(2,3,1)$ and $(3,1,2)$, so the answer is $2$.

Sample Input 2

5 2

Sample Output 2

4

Sample Input 3

98 5

Sample Output 3

809422418

update @ 2024/3/10 08:46:58