P8240 [AGM 2022 Qualification Round] Uranium Theft Plan

You are a thief. You decide to steal some uranium so that you can grow bigger quickly in the game Digdig.io. You have a map. This mine is an undirected graph with $n$ vertices and $m$ edges. There are $K$ guards protecting the mine. The $i$-th guard stays at vertex $P_i$. You have stolen $x$ kilograms of uranium, and you plan to choose a path to move from vertex $S$ to vertex $T$. If $x>0$, then during the transfer, you must ensure that at any moment, your distance to every guard is greater than $x$. Otherwise, you will be discovered. Obviously, you will not steal only once. You need to steal uranium $Q$ times. Each time, given $S$ and $T$, ask for the maximum number of kilograms of uranium you can steal.

The first line contains two integers $n,m$. The next $m$ lines each contain three integers $x,y,z$, meaning there is an undirected edge of length $z$ between $x$ and $y$. The next line contains an integer $K$. The following line contains $K$ integers $P_i$. Then comes a positive integer $Q$. The next $Q$ lines each contain two integers $S,T$.

Output $Q$ lines, each containing one integer as the answer. If it is impossible to complete the theft task, output $0$.

#### Constraints For $100\%$ of the testdata, it is guaranteed that $1\leq n,K,Q\leq 10^5$, $1\leq m\leq 2\times 10^5$, $1\leq x,y,P_i\leq n$, $1\leq z\leq 10^9$, and $S\neq T$. #### Notes Translated from [AGM 2022 Qualification Round L Uranium](https://judge.agm-contest.com/public/problems/13/text)。 Translated by ChatGPT 5