A Perfect Problem

称一个序列为**好序列**当且仅当这个序列的 $\max\times \min\ge sum$，其中 $sum$ 是序列元素和。 给定 $n,M$，求长度为 $n$，每个数在 $[1,n+1]$ 范围内，每个**非空子序列**（包含序列本身）都是好序列的整数序列个数，对 $M$ 取模。 $1\le n\le 200$，$10^8\le M\le 10^9$，保证 $M$ 为素数。

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 $ .

2 998244353

4

4 100000007

32

69 999999937

456886663

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 $ .