CF2084A Max and Mod

You are given an integer $ n $ . Find any permutation $ p $ of length $ n $ $ ^{\text{∗}} $ such that: - For all $ 2 \le i \le n $ , $ \max(p_{i - 1}, p_i) \bmod i $ $ ^{\text{†}} $ $ = i - 1 $ is satisfied. If it is impossible to find such a permutation $ p $ , output $ -1 $ . $ ^{\text{∗}} $ 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). $ ^{\text{†}} $ $ x \bmod y $ denotes the remainder from dividing $ x $ by $ y $ .

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 99 $ ). The description of the test cases follows. The first line of each test case contains a single integer $ n $ ( $ 2 \le n \le 100 $ ).

For each test case: - If such a permutation $ p $ doesn't exist, output a single integer $ -1 $ . - Otherwise, output $ n $ integers $ p_1, p_2, \ldots, p_n $ — the permutation $ p $ you've found. If there are multiple answers, output any of them.

In the first test case, it is impossible to find such a permutation $ p $ , so you should output $ -1 $ . In the fourth test case, $ p = [1, 5, 2, 3, 4] $ satisfies the condition: - For $ i = 2 $ , $ \max(p_1, p_2) = 5 $ and $ 5 \bmod 2 = 1 $ . - For $ i = 3 $ , $ \max(p_2, p_3) = 5 $ and $ 5 \bmod 3 = 2 $ . - For $ i = 4 $ , $ \max(p_3, p_4) = 3 $ and $ 3 \bmod 4 = 3 $ . - For $ i = 5 $ , $ \max(p_4, p_5) = 4 $ and $ 4 \bmod 5 = 4 $ .