CF2210A.A Simple Sequence

You are given an integer $ n $ . You need to construct a permutation $ ^{\text{∗}} $ $ a_1, a_2, \ldots, a_n $ using integers from $ 1 $ to $ n $ such that the following condition is satisfied:

$ a_1 \bmod a_2 \ge a_2 \bmod a_3 \geq \ldots \ge a_{n-1} \bmod a_{n}, $$$ where $ u $ mod $ v $ denotes the remainder of dividing $ u $ by $ v $ . If multiple valid permutations exist, you may output any of them. It can be shown that a valid permutation always exists for every $ n \ge 2 $ . $ ^{\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 first line of each test case contains a single integer $ n $ ( $ 2 \le n \le 100 $ ).

For each test case, output on a single line $ n $ space-separated integers $ a_1, a_2, \ldots a_n $ .

If multiple valid permutations exist, you may output any of them.

In the second test case, $ 2 \bmod 3 \ge 3 \bmod 1 $ , so the permutation $ [2, 3, 1] $ is valid.

In the third test case, $ 2 \bmod 4 \ge 4 \bmod 3 \ge 3 \bmod 1 $ , so the permutation $ [2, 4, 3, 1] $ is valid.