P10002 [CTT Mutual Test 2023] Tree Hashing

This is a [template problem](https://uoj.ac/problem/763). Given positive integers $n, q, mod$. It is guaranteed that $mod$ is a prime number. For a rooted tree $T$ with root at node $1$, let $s(T)$ be the maximum number of pairwise non-isomorphic subtrees that can be chosen from this tree (that is, the number of essentially different subtrees of this tree). Then the weight of this tree is $w(T) = q^{s(T)}$. For every $1 \le m \le n$, output, modulo $mod$, the sum of weights of all labeled trees of size $m$ with root at $1$. Two rooted trees $T_1$ and $T_2$ are isomorphic if and only if they have the same size, and there exists a vertex permutation $\sigma$ such that in $T_1$, $i$ is an ancestor of $j$ if and only if in $T_2$, $\sigma(i)$ is an ancestor of $\sigma(j)$.

One line with two integers, representing $n, q, mod$.

Output $n$ lines. Line $m$ gives the answer for $m$ nodes.

#### Sample Explanation 1 When $n = 3, q = 2, mod = 998244353$, there are three different labeled trees with three nodes and root $1$. Two of them satisfy $w(T) = 2^3$, and the other one satisfies $w(T) = 2^2$. Therefore, the answer is $(2 \times 2^3 + 2^2) \bmod 998244353 = 20$. #### Constraints and Notes For all testdata, it is guaranteed that $n = 100, 10^8 \le mod \le 1.01 \times 10^9, 1 \le q < mod$, and $mod$ is a prime number. This problem has $1$ subtask, and each subtask is worth $100$ points. Your score for each subtask is the minimum score among all test points in that subtask. **You must output $n$ numbers according to the output format, but you are allowed to output incorrect answers**. If you output $c$ correct answers, your score is calculated as follows: - For $0 \le c \le 20$, your score is $2c$ points; - For $21 \le c \le 60$, your score is $c + 20$ points. - For $61 \le c \le 100$, your score is $\lfloor \frac{c}{2}\rfloor + 50$ points. Time limit: $\texttt{4s}$. Memory limit: $\texttt{2048MB}$. You can use the following code to speed up your modulo operations. ```cpp struct fastmod { typedef unsigned long long u64; typedef __uint128_t u128; int m; u64 b; fastmod(int m) : m(m), b(((u128)1 > 64; int r = a - q * m; return r < m ? r : r - m; } } z(2); void solve() { long long mod = 998244353, qwq = 1e9; z = fastmod(mod); cout