CF1603E.A Perfect Problem

A sequence of integers $b_1, b_2, \ldots, b_m$ is called good if $max(b_1, b_2, \ldots, b_m) \cdot min(b_1, b_2, \ldots, b_m) \ge b_1 + b_2 + \ldots + b_m$.

A sequence of integers $a_1, a_2, \ldots, a_n$ is called perfect if every non-empty subsequence of $a$ is good.

YouKn0wWho has two integers $n$ and $M$, $M$ is prime. Help him find the number, modulo $M$, of perfect sequences $a_1, a_2, \ldots, a_n$ such that $1 \le a_i \le n + 1$ for each integer $i$ from $1$ to $n$.

A sequence $d$ is a subsequence of a sequence $c$ if $d$ can be obtained from $c$ by deletion of several (possibly, zero or all) elements.

一个整数序列 $b_1, b_2, \ldots, b_m$ 被称为好序列，若满足

$$\max(b_1, b_2, \ldots, b_m) \cdot \min(b_1, b_2, \ldots, b_m) \ge b_1 + b_2 + \ldots + b_m.$$

一个整数序列 $a_1, a_2, \ldots, a_n$ 被称为完美序列，若其每个非空子序列都是好序列。

YouKn0wWho 给出了两个整数 $n$ 和 $M$，其中 $M$ 是质数。请帮助他计算满足以下条件的完美序列 $a_1, a_2, \ldots, a_n$ 的个数（对 $M$ 取模）：对每个 $i = 1, 2, \ldots, n$，均有 $1 \le a_i \le n + 1$。

序列 $d$ 是序列 $c$ 的一个子序列，当且仅当 $d$ 可通过从 $c$ 中删除若干（可能为零个或全部）元素而得到。

The first and only line of the input contains two space-separated integers $n$ and $M$ ($1 \le n \le 200$; $10^8 \le M \le 10^9$). It is guaranteed that $M$ is prime.

输入仅有一行，包含两个以空格分隔的整数 $n$ 和 $M$（$1 \le n \le 200$；$10^8 \le M \le 10^9$）。保证 $M$ 是质数。

Print a single integer — the number of perfect sequences modulo $M$.

输出一个整数——模 $M$ 意义下的完美序列的数量。

In the first test case, the perfect sequences are $[2, 2]$, $[2, 3]$, $[3, 2]$ and $[3, 3]$.

In the second test case, some of the perfect sequences are $[3, 4, 3, 5]$, $[4, 5, 4, 4]$, $[4, 5, 5, 5]$ etc. One example of a sequence which is not perfect is $[2, 3, 3, 4]$, because, for example, the subsequence $[2, 3, 4]$ is not an good as $2 \cdot 4 \lt 2 + 3 + 4$.

在第一个测试用例中，完美序列有 $[2, 2]$、$[2, 3]$、$[3, 2]$ 和 $[3, 3]$。

在第二个测试用例中，部分完美序列包括 $[3, 4, 3, 5]$、$[4, 5, 4, 4]$、$[4, 5, 5, 5]$ 等。一个非完美序列的例子是 $[2, 3, 3, 4]$，因为例如其子序列 $[2, 3, 4]$ 并不“好”，满足 $2 \cdot 4 \lt 2 + 3 + 4$。