Solve the programming task below in a Python markdown code block.
Read problem statements in [Mandarin], [Bengali], [Russian], and [Vietnamese] as well.

You are given a sequence A_{1}, A_{2}, \ldots, A_{N} which contains pairwise distinct elements and a sequence B_{1}, B_{2}, \ldots, B_{N}, which also contains pairwise distinct elements (but not necessarily distinct from elements of A). For each valid i, 1 ≤ A_{i}, B_{i} ≤ 2 \cdot N.

You may rotate B as many times as you want. A rotation consists of moving the first element of the sequence to the end. Afterwards, let's define a sequence C_{1}, C_{2}, \ldots, C_{N} as C_{i} = (A_{i} + B_{i}) \% N for each valid i.

There are N possible sequences C. Find the lexicographically smallest of these sequences.

Note: A sequence x is lexicographically smaller than a different sequence y if x_{i} < y_{i}, where i is the smallest valid index where the sequences x and y differ.

------ Input Format ------ 

- The first line of the input contains a single integer T denoting the number of test cases. The description of T test cases follows.
- The first line of each test case contains a single integer N.
- The second line contains N space-separated integers A_{1}, A_{2}, \ldots, A_{N}. 
- The third line contains N space-separated integers B_{1}, B_{2}, \ldots, B_{N}. 

------ Output Format ------ 

For each test case, print a single line containing N space-separated integers C_{1}, C_{2}, \ldots, C_{N} denoting the lexicographically smallest sequence.

------ Constraints ------ 

$1 ≤ T ≤ 100$
$1 ≤ N ≤ 10^{5}$
$1 ≤ A_{i}, B_{i} ≤ 2 \cdot N$ for each valid $i$
- the sum of $N$ over all test cases does not exceed $2 \cdot 10^{5}$

------ subtasks ------ 

Subtask #1 (100 points): original constraints

----- Sample Input 1 ------ 
1
3
1 4 5
1 3 4
----- Sample Output 1 ------ 
1 2 0
----- explanation 1 ------ 
Example case 1: After rotating $B$ once, it becomes $(3,4,1)$. Now $C = (1,2,0)$. This is the lexicographically smallest of all possible sequences $C$.