A15884 | Twin Permutations

You are given a permutation $^\dagger$ $a$ of length $n$ .

Find any permutation $b$ of length $n$ such that $a_1+b_1 \le a_2+b_2 \le a_3+b_3 \le \ldots \le a_n+b_n$ .

It can be proven that a permutation $b$ that satisfies the condition above always exists.

$^\dagger$ A permutation of length $n$ is an array consisting of $n$ distinct integers from $1$ to $n$ in arbitrary order. For example, $[2,3,1,5,4]$ is a permutation, but $[1,2,2]$ is not a permutation ( $2$ appears twice in the array), and $[1,3,4]$ is also not a permutation ( $n=3$ but there is $4$ in the array).

Each test contains multiple test cases. The first line of input contains a single integer $t$ ( $1 \le t \le 2000$ ) — the number of test cases. The description of test cases follows.

The first line of each test case contains a single integer $n$ ( $1 \le n \le 100$ ) — the length of permutations $a$ and $b$ .

The second line of each test case contains $n$ distinct integers $a_1,a_2,\ldots,a_n$ ( $1 \le a_i \le n$ ) — the elements of permutation $a$ . All elements of $a$ are distinct.

Note that there is no bound on the sum of $n$ over all test cases.

For each test case, output any permutation $b$ which satisfies the constraints mentioned in the statement. It can be proven that a permutation $b$ that satisfies the condition above always exists.