Fast Spanning Tree

Wang Xiuhan has an initially empty undirected graph on $n$ vertices.

Each vertex has a weight, which is a non-negative integer.

He also has $m$ tuples $(a_i, b_i, s_i)$, where $1 \le a_i, b_i \le n$, $a_i \ne b_i$, and $s_i$ is a non-negative integer.

After that, he starts the following process:

• If there is no $i$ such that $a_i$ and $b_i$ lie in different connected components and (total weight of the component of $a_i$) + (total weight of the component of $b_i$) $\ge s_i$, the process ends.
• Otherwise, he chooses the smallest such $i$, adds an edge between $a_i$ and $b_i$, writes $i$ in the notepad, and repeats the process on the larger graph.

The process is finished, and then a misfortune happens: someone stole his notepad! Can you help him restore all the numbers efficiently?

The first line contains two integers $n$ and $m$: the number of vertices in the graph and the number of tuples ($1 \le n, m \le 300\,000$).

The second line contains $n$ space-separated integers $w_1, w_2, \ldots, w_n$, the weights of the vertices ($0 \le w_i \le 10^6$).

Each of the next $m$ lines contains three integers $a_i$, $b_i$, $s_i$ ($1 \le a_i, b_i \le n$, $a_i \ne b_i$, $0 \le s_i \le 10^6$).

On the first line, print the number of integers written in the notepad. On the next line, print all these integers in the order he wrote them.