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. Input Format: 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 Format: For each of $$$t$$$ test cases print $$$n$$$ positive integers $$$d_1, d_2, \dots, d_n$$$ — the duration of each task. 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.