Vlad and the Mountains

Description:

Input:

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:

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.

Sample Input:

2
7 7
1 5 3 4 2 4 1
1 4
4 3
3 6
3 2
2 5
5 6
5 7
5
1 1 3
6 2 0
4 7 0
1 7 4
1 7 2
6 5
4 7 6 2 5 1
1 3
5 3
1 5
2 4
6 2
5
1 5 1
1 3 1
1 2 1000
6 2 6
6 2 5

Sample Output:

YES
NO
YES
YES
NO

YES
NO
NO
YES
NO

Sample Input:

2
3 2
1 3 9
1 2
2 3
5
1 1 1
3 2 2
1 1 2
3 3 0
1 2 1
3 3
1 4 1
1 2
2 3
1 3
5
3 3 9
1 3 6
1 1 2
3 3 6
3 3 4

Sample Output:

YES
YES
YES
YES
NO

YES
YES
YES
YES
YES

Sample Input:

1
6 10
7 9 2 10 8 6
4 2
6 1
4 5
3 5
6 4
1 3
2 6
6 5
1 2
3 6
5
4 4 8
3 3 1
5 5 9
2 1 7
6 6 10

Sample Output:

YES
YES
YES
YES
YES