platinum_Infinite_Adventure — USACO February_Contest
Task type: batch | Time limit: 2 s | Memory limit: 512 MB | Difficulty: 24
Algorithms: functional graph, lowest common ancestor, modular arithmetic

**Note: The memory limit for this problem is 512MB, twice the default.**
Bessie is planning an infinite adventure in a land with $N$
($1\leq N \leq 10^5$) cities. In each city $i$, there is a portal, as well as a
cycling time $T_i$.  All $T_i$'s are powers of $2$, and
$T_1 + \cdots + T_N \leq 10^5$. If you enter city $i$'s portal on day $t$, then
you instantly exit the portal in city
$c_{i, t\bmod{T_i}}$.
Bessie has $Q$ ($1\leq Q \leq 5\cdot 10^4$) plans for her trip, each of which
consists of a tuple $(v, t, \Delta)$. In each plan, she will start in city $v$
on day $t$. She will then do the following $\Delta$ times: She will follow the
portal in her current city, then wait one day. For each of her plans, she wants
to know what city she will end up in.
INPUT FORMAT (input arrives from the terminal / stdin):
The first line contains two space-separated integers: $N$, the number of nodes,
and $Q$, the number of queries.
The second line contains $N$ space-separated integers: $T_1, T_2, \ldots, T_N$
($1\leq T_i$, $T_i$ is a power of $2$, and $T_1 + \cdots + T_N \leq 10^5$).
For $i = 1, 2, \ldots, N$, line $i+2$ contains $T_i$ space-separated positive
integers, namely $c_{i, 0}, \ldots, c_{i, T_i-1}$ ($1\leq c_{i, t} \leq N$).
For $j = 1, 2, \ldots, Q$, line $j+N+2$ contains three space-separated positive
integers, $v_j, t_j, \Delta_j$ ($1\leq v_j \leq N$, $1\leq t_j \leq 10^{18}$,
and $1\leq \Delta_j \leq 10^{18}$) representing the $j$th query.
OUTPUT FORMAT (print output to the terminal / stdout):
Print $Q$ lines. The $j$th line must contain the answer to the $j$th query.
SAMPLE INPUT:
5 4
1 2 1 2 8
2
3 4
4
2 3
5 5 5 5 5 1 5 5
2 4 3
3 3 6
5 3 2
5 3 7
SAMPLE OUTPUT:
2
2
5
4
Bessie's first three adventures proceed as follows:
In the first adventure, she goes from city $2$ at time $4$ to city $3$ at time $5$, to city $4$ at time $6$, to city $2$ at time $7$.
In the second adventure, she goes from city $3$ at time $3$ to city $4$ at time $4$, to city $2$ at time $5$, to city $4 $ at time $6$, to city $2$ at time $7$, to city $4$ at time $8$, to city $2$ at time $9$.
In the third adventure, she goes from city $5$ at time $3$ to city $5$ at time $4$, to city $5$ at time $5$.
SAMPLE INPUT:
5 5
1 2 1 2 8
2
3 4
4
2 3
5 5 5 5 5 1 5 5
2 4 3
3 2 6
5 3 2
5 3 7
5 3 1000000000000000000
SAMPLE OUTPUT:
2
3
5
4
2
SCORING:
Input 3: $\Delta_j \leq 2\cdot 10^2$.
Inputs 4-5: $N, \sum T_j\leq 2\cdot 10^3$.
Inputs 6-8: $N, \sum T_j\leq 10^4$.
Inputs 9-18: No additional constraints.
Problem credits: Brandon Wang

Starter code: