#P1690C. Restoring the Duration of Tasks
Restoring the Duration of Tasks
Description
Recently, Polycarp completed $n$ successive tasks.
For each completed task, the time $s_i$ is known when it was given, no two tasks were given at the same time. Also given is the time $f_i$ when the task was completed. For each task, there is an unknown value $d_i$ ($d_i>0$) — duration of task execution.
It is known that the tasks were completed in the order in which they came. Polycarp performed the tasks as follows:
- As soon as the very first task came, Polycarp immediately began to carry it out.
- If a new task arrived before Polycarp finished the previous one, he put the new task at the end of the queue.
- When Polycarp finished executing the next task and the queue was not empty, he immediately took a new task from the head of the queue (if the queue is empty — he just waited for the next task).
Find $d_i$ (duration) of each task.
The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.
The descriptions of the input data sets follow.
The first line of each test case contains one integer $n$ ($1 \le n \le 2 \cdot 10^5$).
The second line of each test case contains exactly $n$ integers $s_1 < s_2 < \dots < s_n$ ($0 \le s_i \le 10^9$).
The third line of each test case contains exactly $n$ integers $f_1 < f_2 < \dots < f_n$ ($s_i < f_i \le 10^9$).
It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.
For each of $t$ test cases print $n$ positive integers $d_1, d_2, \dots, d_n$ — the duration of each task.
Input
The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.
The descriptions of the input data sets follow.
The first line of each test case contains one integer $n$ ($1 \le n \le 2 \cdot 10^5$).
The second line of each test case contains exactly $n$ integers $s_1 < s_2 < \dots < s_n$ ($0 \le s_i \le 10^9$).
The third line of each test case contains exactly $n$ integers $f_1 < f_2 < \dots < f_n$ ($s_i < f_i \le 10^9$).
It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.
Output
For each of $t$ test cases print $n$ positive integers $d_1, d_2, \dots, d_n$ — the duration of each task.
Samples
4
3
0 3 7
2 10 11
2
10 15
11 16
9
12 16 90 195 1456 1569 3001 5237 19275
13 199 200 260 9100 10000 10914 91066 5735533
1
0
1000000000
2 7 1
1 1
1 183 1 60 7644 900 914 80152 5644467
1000000000
Note
First test case:
The queue is empty at the beginning: $[ ]$. And that's where the first task comes in. At time $2$, Polycarp finishes doing the first task, so the duration of the first task is $2$. The queue is empty so Polycarp is just waiting.
At time $3$, the second task arrives. And at time $7$, the third task arrives, and now the queue looks like this: $[7]$.
At the time $10$, Polycarp finishes doing the second task, as a result, the duration of the second task is $7$.
And at time $10$, Polycarp immediately starts doing the third task and finishes at time $11$. As a result, the duration of the third task is $1$.
An example of the first test case.