A11284. Distance Learning Courses in MAC

The New Year has arrived in the Master's Assistance Center, which means it's time to introduce a new feature!

Now students are given distance learning courses, with a total of $n$ courses available. For the $i$ -th distance learning course, a student can receive a grade ranging from $x_i$ to $y_i$ .

However, not all courses may be available to each student. Specifically, the $j$ -th student is only given courses with numbers from $l_j$ to $r_j$ , meaning the distance learning courses with numbers $l_j, l_j + 1, \ldots, r_j$ .

The creators of the distance learning courses have decided to determine the final grade in a special way. Let the $j$ -th student receive grades $c_{l_j}, c_{l_j + 1}, \ldots, c_{r_j}$ for their distance learning courses. Then their final grade will be equal to $c_{l_j}$ $|$ $c_{l_j + 1}$ $|$ $\ldots$ $|$ $c_{r_j}$ , where $|$ denotes the [bitwise OR](https://en.wikipedia.org/wiki/Bitwise_operation#OR) operation.

Since the chatbot for solving distance learning courses is broken, the students have asked for your help. For each of the $q$ students, tell them the maximum final grade they can achieve.

Each test consists of multiple test cases. The first line contains a single integer $t$ ( $1 \leq t \leq 2 \cdot 10^4$ ) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer $n$ ( $1 \le n \le 2 \cdot 10^5$ ) — the number of distance learning courses.

Each of the following $n$ lines contains two integers $x_i$ and $y_i$ ( $0 \le x_i \le y_i < 2^{30}$ ) — the minimum and maximum grade that can be received for the $i$ -th course.

The next line contains a single integer $q$ ( $1 \le q \le 2\cdot10^5$ ) — the number of students.

Each of the following $q$ lines contains two integers $l_j$ and $r_j$ ( $1 \le l_j \le r_j \le n$ ) — the minimum and maximum course numbers accessible to the $j$ -th student.

It is guaranteed that the sum of $n$ over all test cases and the sum of $q$ over all test cases do not exceed $2\cdot10^5$ .

For each test case, output $q$ integers, where the $j$ -th integer is the maximum final grade that the $j$ -th student can achieve.

In the first test case:

1. The maximum grade for the first student is $1$ :
- On the first distance learning course, he will receive a grade of $1$ .

Therefore, the final grade is $1$ .
2. The maximum grade for the second student is $5$ :
- On the first distance learning course, he will receive a grade of $1$ .
- On the second distance learning course, he will receive a grade of $4$ .

Therefore, the final grade is $1$ $|$ $4$ $=$ $5$ .
3. The maximum grade for the third student is $4$ :
- On the second distance learning course, he will receive a grade of $4$ .

Therefore, the final grade is $4$ .

In the second test case:

1. The maximum grade for the first student is $15$ :
- On the first distance learning course, he will receive a grade of $7$ .
- On the second distance learning course, he will receive a grade of $4$ .
- On the third distance learning course, he will receive a grade of $8$ .

Therefore, the final grade is $7$ $|$ $4$ $|$ $8$ $=$ $15$ .
2. The maximum grade for the second student is $11$ :
- On the third distance learning course, he will receive a grade of $9$ .
- On the fourth distance learning course, he will receive a grade of $2$ .

Therefore, the final grade is $9$ $|$ $2$ $=$ $11$ .