Cactus

A cactus graph is a connected undirected graph with no self-loops or multiple edges in which each edge belongs to at most one simple cycle.

You are given a cactus graph $G$ with $N$ vertices, numbered from $1$ to $N$, and $M$ edges. The $i$-th edge connects vertices $a_i$ and $b_i$, and its cost is $c_i$.

The cost of a simple path in $G$ is the bitwise XOR of the costs of all edges on that path.

Answer $Q$ queries of the form "$x_i$ $y_i$ $k_i$". Consider the costs of all simple paths connecting vertices $x_i$ and $y_i$, remove duplicate values, sort them in ascending order, and output the $k_i$-th element. If there are fewer than $k_i$ distinct values, output $-1$.

The first line contains two integers $N$ and $M$, the number of vertices and edges ($2 \le N \le 10^5$, $N-1 \le M \le 2 \cdot 10^5$).

Each of the next $M$ lines contains three integers $a_i$, $b_i$, and $c_i$ ($1 \le a_i, b_i \le N$, $a_i \ne b_i$, $0 \le c_i < 2^{30}$).

The next line contains an integer $Q$, the number of queries ($1 \le Q \le 2 \cdot 10^5$).

Each of the next $Q$ lines contains three integers $x_i$, $y_i$, and $k_i$ ($1 \le x_i, y_i \le N$, $x_i \ne y_i$, $1 \le k_i \le 2^{30}$).

For each query, print one integer on its own line: the answer to that query.