A14571. 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.

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.

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

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 $2 \cdot 4 < 2 + 3 + 4$ .