Description:
Vlad decided to go on a trip to the mountains. He plans to move between $$$n$$$ mountains, some of which are connected by roads. The $$$i$$$-th mountain has a height of $$$h_i$$$.
If there is a road between mountains $$$i$$$ and $$$j$$$, Vlad can move from mountain $$$i$$$ to mountain $$$j$$$ by spending $$$h_j - h_i$$$ units of energy. If his energy drops below zero during the transition, he will not be able to move from mountain $$$i$$$ to mountain $$$j$$$. Note that $$$h_j - h_i$$$ can be negative and then the energy will be restored.
Vlad wants to consider different route options, so he asks you to answer the following queries: is it possible to construct some route starting at mountain $$$a$$$ and ending at mountain $$$b$$$, given that he initially has $$$e$$$ units of energy?
Input Format:
The first line of the input contains an integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.
The descriptions of the test cases follow.
The first line of each test case contains two numbers $$$n$$$ and $$$m$$$ ($$$2 \le n \le 2 \cdot 10^5$$$, $$$1 \le m \le \min(\frac{n\cdot(n - 1)}{2}, 2 \cdot 10^5)$$$) — the number of mountains and the number of roads between them, respectively.
The second line contains $$$n$$$ integers $$$h_1, h_2, h_3, \dots, h_n$$$ ($$$1 \le h_i \le 10^9$$$) — the heights of the mountains.
The next $$$m$$$ lines contain two integers $$$u$$$ and $$$v$$$ ($$$1 \le u, v \le n$$$, $$$u \ne v$$$) — the numbers of the mountains connected by a road. It is guaranteed that no road appears twice.
The next line contains an integer $$$q$$$ ($$$1 \le q \le 2 \cdot 10^5$$$) — the number of queries.
The following $$$q$$$ lines contain three numbers $$$a$$$, $$$b$$$, and $$$e$$$ ($$$1 \le a, b \le n$$$, $$$0 \le e \le 10^9$$$) — the initial and final mountains of the route, and the amount of energy, respectively.
It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$. The same guarantee applies to $$$m$$$ and $$$q$$$.
Output Format:
For each query, output "YES" if Vlad can construct a route from mountain $$$a$$$ to mountain $$$b$$$, and "NO" otherwise.
You can output the answer in any case (for example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as a positive answer).
In the examples below, the answers for different test cases are separated by an empty line, which you do not need to output.
Note:
None