CF2188A Divisible Permutation

You are given an integer $ n $ . Construct a permutation $ ^{\text{∗}} $ $ p $ of length $ n $ satisfying the following condition: - $ \lvert p_i - p_{i+1} \rvert $ is divisible by $ i $ for every $ 1 \le i \le n-1 $ . It can be proven that such a permutation always exists under the constraints of the problem. $ ^{\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).

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 100 $ ). The description of the test cases follows. The only line of each test case contains a single integer $ n $ ( $ 2 \le n \le 100 $ ) — the length of the permutation $ p $ to be constructed.

For each test case, output $ n $ integers $ p_1,p_2,\ldots,p_n $ ( $ 1 \le p_i \le n $ , all $ p_i $ -s are distinct) — the permutation you constructed. If there are multiple valid permutations, you may output any of them.

In the first test case, $ p=[1,2] $ satisfies the condition because $ \lvert p_1-p_2\rvert=\lvert 1-2\rvert=1 $ , which is divisible by $ 1 $ . In the second test case, $ p=[2,3,1] $ satisfies the condition because: - $ \lvert p_1-p_2\rvert=\lvert 2-3\rvert=1 $ , which is divisible by $ 1 $ , and - $ \lvert p_2-p_3\rvert=\lvert 3-1\rvert=2 $ , which is divisible by $ 2 $ .