CF2147B Multiple Construction

You are given an integer $ n $ . Your task is to construct an array of length $ 2 \cdot n $ such that: - Each integer from $ 1 $ to $ n $ appears exactly twice in the array. - For each integer $ x $ ( $ 1 \le x \le n $ ), the distance between the two occurrences of $ x $ is a multiple of $ x $ . In other words, if $ p_x $ and $ q_x $ are the indices of the two occurrences of $ x $ , $ | q_x - p_x | $ must be divisible by $ x $ . It can be shown that a solution always exists.

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 10^4 $ ). The description of the test cases follows. Each of the next $ t $ lines contains a single integer $ n $ ( $ 1 \le n \le 2 \cdot 10^{5} $ ). It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2 \cdot 10^{5} $ .

For each test case, print a line containing $ 2 \cdot n $ integers — the array that satisfies the given conditions. If there are multiple valid answers, print any of them.

[Visualizer link](https://codeforces.com/assets/contests/2147/B_RlbLXHyL5DuDqDlx4DG1.html) In the first test case: - The number $ 1 $ appears at positions $ 1 $ and $ 3 $ : the distance is $ 2 $ , which is divisible by $ 1 $ . - The number $ 2 $ appears at positions $ 2 $ and $ 4 $ : the distance is $ 2 $ , which is divisible by $ 2 $ . In the second test case: - The number $ 1 $ appears at positions $ 1 $ and $ 3 $ : the distance is $ 2 $ , which is divisible by $ 1 $ . - The number $ 2 $ appears at positions $ 4 $ and $ 6 $ : the distance is $ 2 $ , which is divisible by $ 2 $ . - The number $ 3 $ appears at positions $ 2 $ and $ 5 $ : the distance is $ 3 $ , which is divisible by $ 3 $ . In the third test case, the two occurrences of $ 1 $ are at positions $ 1 $ and $ 2 $ , so the distance between them is $ 1 $ , which is a multiple of $ 1 $ .