#P1935E. Distance Learning Courses in MAC
Distance Learning Courses in MAC
Description
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 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.
Input
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 $2\cdot10^5$.
Output
For each test case, output $q$ integers, where the $j$-th integer is the maximum final grade that the $j$-th student can achieve.
3
2
0 1
3 4
3
1 1
1 2
2 2
4
1 7
1 7
3 10
2 2
5
1 3
3 4
2 3
1 4
1 2
6
1 2
2 2
0 1
1 1
3 3
0 0
4
3 4
5 5
2 5
1 2
1 5 4
15 11 15 15 7
1 3 3 3
Note
In the first test case:
- The maximum grade for the first student is $1$:
- On the first distance learning course, he will receive a grade of $1$.
- 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 $4$.
- The maximum grade for the third student is $4$:
- On the second distance learning course, he will receive a grade of $4$.
In the second test case:
- 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 $8$.
- 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 $2$.