Salaj

Given two integers $V$ and $E$, an array $A$ of length $E$ is a valid connectivity history array (CHA) if there is a directed graph with $V$ vertices and $E$ edges and a permutation $P$ of length $E$ such that, starting from an empty graph on $V$ vertices and adding edges in the order given by $P$, every $1 \le i \le E$ satisfies: after the $P[i]$-th edge is added, the number of strongly connected components is $A[i]$. The graph may not contain self-loops or multiple edges, but if the edge $(x, y)$ exists, the edge $(y, x)$ may also exist. For example, with $V = 3$ and $E = 3$, $A = [3, 3, 3]$ is valid because the graph $\{(1, 2), (1, 3), (2, 3)\}$ always has three strongly connected components, whatever the order. $A = [3, 3, 1]$ is valid because the graph $\{(1, 2), (2, 3), (3, 1)\}$ added in that order has 3, 3, then 1 strongly connected components. $A = [3, 2, 1]$ is not valid, because no graph with three edges on three vertices has a edge order where the count drops after each added edge.

The first line contains $Q$, the number of queries ($Q \le 10$). Each of the next $Q$ lines contains three integers $V_i$, $MAX_i$, and $MOD_i$ ($1 \le V_i \le 50$, $1 \le MAX_i \le V_i(V_i - 1)$, $1 \le MOD_i \le 10^9$).

For each query, print one line with $MAX_i$ integers. The $j$-th integer is the number of valid CHAs for the pair $(V_i, j)$, taken modulo $MOD_i$, where $1 \le j \le MAX_i$.