CF1851G.Vlad and the Mountains

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?

弗拉德决定去山区旅行。他计划在 $n$ 座山之间移动，其中一些山由道路连接。第 $i$ 座山的高度为 $h_i$。

如果山 $i$ 与山 $j$ 之间存在一条道路，则弗拉德可以从山 $i$ 移动到山 $j$，消耗 $h_j - h_i$ 单位的能量。若在移动过程中他的能量降至零以下，则他将无法从山 $i$ 移动到山 $j$。注意，$h_j - h_i$ 可能为负数，此时能量将得到恢复。

弗拉德希望考虑不同的路线方案，因此请你回答如下查询：给定初始能量为 $e$，是否存在一条从山 $a$ 出发、到达山 $b$ 的路径？

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 $q$.

输入的第一行包含一个整数 $t$（$1 \le t \le 10^4$）—— 表示测试用例的数量。

随后是各测试用例的描述。

每个测试用例的第一行包含两个整数 $n$ 和 $m$（$2 \le n \le 2 \cdot 10^5$，$1 \le m \le \min(\frac{n\cdot(n - 1)}{2}, 2 \cdot 10^5)$）—— 分别表示山峰的数量以及山峰之间的道路数量。

第二行包含 $n$ 个整数 $h_1, h_2, h_3, \dots, h_n$（$1 \le h_i \le 10^9$）—— 表示各山峰的高度。

接下来的 $m$ 行每行包含两个整数 $u$ 和 $v$（$1 \le u, v \le n$，$u \ne v$）—— 表示由一条道路连接的两座山峰的编号。保证不会出现重复的道路。

接下来一行包含一个整数 $q$（$1 \le q \le 2 \cdot 10^5$）—— 表示查询的数量。

接下来的 $q$ 行每行包含三个数 $a$、$b$ 和 $e$（$1 \le a, b \le n$，$0 \le e \le 10^9$）—— 分别表示路径的起点山峰、终点山峰以及能量值。

保证所有测试用例中 $n$ 的总和不超过 $2 \cdot 10^5$；对 $m$ 和 $q$ 同样有此保证。

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.

对于每个查询，如果弗拉德能够构建一条从山 $a$ 到山 $b$ 的路径，则输出 "YES"；否则输出 "NO"。

答案的大小写不限（例如，字符串 "yEs"、"yes"、"Yes" 和 "YES" 均被视为肯定回答）。

在下面的示例中，不同测试用例的答案之间以空行分隔，但你无需输出该空行。