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一、Problem Name

Infinite Adventure

二、Problem Description

Bessie is planning an infinite adventure in a land with $N$ ($1\leq N\leq10^5$) 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 $T_1+\cdots+T_N\leq10^5$. 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 $Q$ ($1\leq Q\leq5\cdot10^4$) 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.

三、Input Format (input arrives from the terminal / stdin)

1. The first line contains two space - separated integers: $N$, the number of nodes, and $Q$, the number of queries.
2. The second line contains $N$ space - separated integers: $T_1,T_2,\cdots,T_N$ ($1\leq T_i$, $T_i$ is a power of $2$, and $T_1+\cdots+T_N\leq10^5$).
3. For $i = 1,2,\cdots,N$, line $i + 2$ contains $T_i$ space - separated positive integers, namely $c_{i,0},\cdots,c_{i,T_i - 1}$ ($1\leq c_{i,t}\leq N$).
4. For $j = 1,2,\cdots,Q$, line $j + N + 2$ contains three space - separated positive integers, $v_j,t_j,\Delta_j$ ($1\leq v_j\leq N$, $1\leq t_j\leq10^{18}$, and $1\leq\Delta_j\leq10^{18}$) representing the $j$th query.

四、Output Format (print output to the终端 / stdout)

Print $Q$ lines. The $j$th line must contain the answer to the $j$th query.

五、Sample Input and Output

Sample Input 1

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 1

2
2
5
4

Explanation: 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 2

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

2
3
5
4
2

六、Scoring Rules

1. Input 3: $\Delta_j\leq2\cdot10^2$.
2. Inputs 4 - 5: $N,\sum T_j\leq2\cdot10^3$.
3. Inputs 6 - 8: $N,\sum T_j\leq10^4$.
4. Inputs 9 - 18: No additional constraints.

Problem credits: Brandon Wang.