A. Twin Permutations
constructive algorithms
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.
In the first test case \(a=[1, 2, 4, 5, 3]\). Then the permutation \(b=[1, 2, 4, 3, 5]\) satisfies the condition because \(1 + 1 \le 2 + 2 \le 4 + 4 \le 5 + 3 \le 3 + 5\).