Yet Another Permutation Problem 2

Set $Q_i=N+1-P_i$ at every position. Because $P$ contains each integer from $1$ to $N$ exactly once, $Q$ also contains each of those integers exactly once. Thus, $Q$ is a permutation.

For every $i$, $P_i+Q_i=N+1$. The sequence of sums is constant, so it is nondecreasing. This construction directly provides the guaranteed answer.

In subtask 1, $P_i=i$, so one may set $Q_i=N+1-i$. In subtask 3, $P_i=N+1-i$, so one may set $Q_i=i$. The general construction solves subtask 2 and the full subtask.

The time complexity for each subtask is $O(T+\sum N)$. Processing input and output sequentially uses $O(1)$ additional space.

Solution written by GPT5