CF1818B Indivisible

You're given a positive integer $ n $ . Find a permutation $ a_1, a_2, \dots, a_n $ such that for any $ 1 \leq l < r \leq n $ , the sum $ a_l + a_{l+1} + \dots + a_r $ is not divisible by $ r-l+1 $ . 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 contains the number of test cases $ t $ ( $ 1 \le t \le 100 $ ). Description of the test cases follows. The first line of each test case contain a single integer $ n $ ( $ 1 \leq n \leq 100 $ ) — the size of the desired permutation.

For each test case, if there is no such permutation print $ -1 $ . Otherwise, print $ n $ distinct integers $ p_1, p_{2}, \dots, p_n $ ( $ 1 \leq p_i \leq n $ ) — a permutation satisfying the condition described in the statement. If there are multiple solutions, print any.

In the first example, there are no valid pairs of $ l < r $ , meaning that the condition is true for all such pairs. In the second example, the only valid pair is $ l=1 $ and $ r=2 $ , for which $ a_1 + a_2 = 1+2=3 $ is not divisible by $ r-l+1=2 $ . in the third example, for $ l=1 $ and $ r=3 $ the sum $ a_1+a_2+a_3 $ is always $ 6 $ , which is divisible by $ 3 $ .