CF1774H Maximum Permutation

Ecrade bought a deck of cards numbered from $ 1 $ to $ n $ . Let the value of a permutation $ a $ of length $ n $ be $ \min\limits_{i = 1}^{n - k + 1}\ \sum\limits_{j = i}^{i + k - 1}a_j $ . Ecrade wants to find the most valuable one among all permutations of the cards. However, it seems a little difficult, so please help him!

The first line contains a single integer $ t $ ( $ 1 \leq t \leq 2 \cdot 10^4 $ ) — the number of test cases. The description of test cases follows. The only line of each test case contains two integers $ n,k $ ( $ 4 \leq k < n \leq 10^5 $ ). It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2 \cdot 10^6 $ .

For each test case, output the largest possible value in the first line. Then in the second line, print $ n $ integers $ a_1,a_2,\dots,a_n $ ( $ 1 \le a_i \le n $ , all $ a_i $ are distinct) — the elements of the permutation that has the largest value. If there are multiple such permutations, output any of them.

In the first test case, $ [1,4,5,3,2] $ has a value of $ 13 $ . It can be shown that no permutations of length $ 5 $ have a value greater than $ 13 $ when $ k = 4 $ . In the second test case, $ [4,2,5,7,8,3,1,6] $ has a value of $ 18 $ . It can be shown that no permutations of length $ 8 $ have a value greater than $ 18 $ when $ k = 4 $ .