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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 $C$.

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