最小环的期望长度 - 题目

#18171. 最小环的期望长度

统计

AI Translation — This statement was translated using AI and may contain inaccuracies. Please refer to the original statement if in doubt.

给定一个正整数 $N$，求 $1$ 到 $N$ 的整数排列中最小环的期望长度。所有排列都是等概率出现的。

设答案为最简分数 $\frac{A}{B}$。输出 $A \cdot B^{-1} \bmod P$，其中 $P$ 是给定的质数。保证 $\gcd(B, P) = 1$。

输入格式

输入仅包含一行，有两个整数 $N$ 和 $P$（$1 \le N \le 10^4$，$10^4 < P \le 10^9 + 33$）。保证 $P$ 是一个质数。

输出格式

在一行中输出该问题的答案。

样例

输入样例 1

2 1000000007

输出样例 1

500000005

输入样例 2

3 1000000007

输出样例 2

666666673

Discussions

About Discussions

The discussion section is only for posting: General Discussions (problem-solving strategies, alternative approaches), and Off-topic conversations.

This is NOT for reporting issues! If you want to report bugs or errors, please use the Issues section below.

Open Discussions 0

No discussions in this category.

Issues

About Issues

If you find any issues with the problem (statement, scoring, time/memory limits, test cases, etc.), you may submit an issue here. A problem moderator will review your issue.

Guidelines:

This is not a place to publish discussions, editorials, or requests to debug your code. Issues are only visible to you and problem moderators.
Do not submit duplicated issues.
Issues must be filed in English or Chinese only.

Active Issues 0

No issues in this category.

Closed/Resolved Issues 0