Yet Another Permutation Problem 2

You are given a permutation $P=(P_1,P_2,\cdots,P_N)$ of the integers from $1$ to $N$.

Construct a permutation $Q=(Q_1,Q_2,\cdots,Q_N)$.

The sequence $P_1+Q_1,P_2+Q_2,\cdots,P_N+Q_N$ must be nondecreasing. In other words, $P_i+Q_i\leq P_{i+1}+Q_{i+1}$ must hold for every $i$ ($1\leq i<N$).

It is guaranteed that such a permutation $Q$ always exists.

The input is given in the following format:

$T$ $\mathrm{case}_1$ $\mathrm{case}_2$ $\vdots$ $\mathrm{case}_T$

Each case is given in the following format:

$N$ $P_1\ P_2\ \cdots\ P_N$

$T$ is the number of test cases. Each case gives the length $N$ and the permutation $P$.

For each test case, print the elements $Q_1,Q_2,\cdots,Q_N$ of any valid permutation $Q$ on one line, separated by spaces.

If multiple valid answers exist, print any of them.

• $1 \leq T \leq 100\,000$.
• $1 \leq N \leq 200\,000$.
• $1 \leq P_i \leq N$ ($1 \leq i \leq N$).
• $P_i\neq P_j$ ($1 \leq i<j \leq N$).
• The sum of $N$ over all test cases is at most $200\,000$.