CF1992C Gorilla and Permutation

Gorilla and Noobish\_Monk found three numbers $ n $ , $ m $ , and $ k $ ( $ m < k $ ). They decided to construct a permutation $ ^{\dagger} $ of length $ n $ . For the permutation, Noobish\_Monk came up with the following function: $ g(i) $ is the sum of all the numbers in the permutation on a prefix of length $ i $ that are not greater than $ m $ . Similarly, Gorilla came up with the function $ f $ , where $ f(i) $ is the sum of all the numbers in the permutation on a prefix of length $ i $ that are not less than $ k $ . A prefix of length $ i $ is a subarray consisting of the first $ i $ elements of the original array. For example, if $ n = 5 $ , $ m = 2 $ , $ k = 5 $ , and the permutation is $ [5, 3, 4, 1, 2] $ , then: - $ f(1) = 5 $ , because $ 5 \ge 5 $ ; $ g(1) = 0 $ , because $ 5 > 2 $ ; - $ f(2) = 5 $ , because $ 3 < 5 $ ; $ g(2) = 0 $ , because $ 3 > 2 $ ; - $ f(3) = 5 $ , because $ 4 < 5 $ ; $ g(3) = 0 $ , because $ 4 > 2 $ ; - $ f(4) = 5 $ , because $ 1 < 5 $ ; $ g(4) = 1 $ , because $ 1 \le 2 $ ; - $ f(5) = 5 $ , because $ 2 < 5 $ ; $ g(5) = 1 + 2 = 3 $ , because $ 2 \le 2 $ . Help them find a permutation for which the value of $ \left(\sum_{i=1}^n f(i) - \sum_{i=1}^n g(i)\right) $ is maximized. $ ^{\dagger} $ A permutation of length $ n $ is an array consisting of $ n $ distinct integers from $ 1 $ to $ n $ in any order. For example, $ [2,3,1,5,4] $ is a permutation, but $ [1,2,2] $ is not a permutation (as $ 2 $ appears twice in the array) and $ [1,3,4] $ is also not a permutation (as $ n=3 $ , but $ 4 $ appears in the array).

The first line contains a single integer $ t $ ( $ 1 \le t \le 10^4 $ ) — the number of test cases. The only line of each case contains three integers $ n $ , $ m $ , $ k $ ( $ 2\le n \le 10^5 $ ; $ 1 \le m < k \le n $ ) — the size of the permutation to be constructed and two integers. It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2 \cdot 10^5 $ .

For each test case, output the permutation — a set of numbers that satisfies the conditions of the problem. If there are multiple solutions, output any of them.

In the first example, $ \left(\sum_{i=1}^n f(i) - \sum_{i=1}^n g(i)\right) = 5 \cdot 5 - (0 \cdot 3 + 1 + 3) = 25 - 4 = 21 $