Counting Phenomenal Arrays

Call an array $[a_1, a_2, \ldots, a_k]$ of positive integers phenomenal if the product of its elements equals the sum of its elements, that is, $a_1 a_2 \ldots a_k = a_1 + a_2 + \ldots + a_k$.

For example, $[2, 2]$ is phenomenal because $2 \cdot 2 = 2 + 2 = 4$. $[3, 1, 2]$ is phenomenal because $3 \cdot 1 \cdot 2 = 3 + 1 + 2 = 6$. However, $[2, 3]$ is not phenomenal, since $2 \cdot 3 \neq 2 + 3$.

Let $f(i)$ denote the number of phenomenal arrays of size $i$. It can be shown that for any fixed $i \ge 2$, there are only finitely many phenomenal arrays of size $i$.

You are given an integer $n$. Find $f(2), f(3), \ldots, f(n)$. Since these numbers can be very large, output each one modulo $P$, where $P$ is a prime given in the input.

The only line of the input contains two integers $n$ and $P$ ($2 \le n \le 2\cdot 10^5$, $10^8 \le P \le 10^9$, $P$ is prime).

Output $n-1$ integers: the values $f(2), f(3), \ldots, f(n)$ modulo $P$.