You are given an integer n representing the number of nodes in a directed graph, labeled from $0$ to n $- 1$, and an integer threshold. You are also given a $2 ext{D}$ integer array edges, where edges[i] $= [A_i, B_i, W_i]$ indicates a directed edge from node $A_i$ to node $B_i$ with weight $W_i$.

Your task is to select a subset of edges such that:

• Node $0$ is reachable from every other node using the selected edges.

• The out-degree of every node in the selected set of edges is at most threshold.

• The maximum weight among all selected edges is minimized.

Return the minimum possible value of the maximum edge weight among the chosen edges. If it is impossible to satisfy these conditions, return $-1$.

Constraints:

• $2 \leq$ n $\leq 10^5$

• $1 \leq$ threshold $\leq$ n $- 1$

• $1 \leq$ edges.length $\leq \min(10^5, \frac{ ext{`n`} \cdot ( ext{`n`} - 1)}{2})$

• edges[i].length $= 3$

• $0 \leq A_i, B_i <$ n

• $A_i \neq B_i$

• $1 \leq W_i \leq 10^6$

• There may be multiple edges between a pair of nodes, but they must have unique weights.

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.