CF1770B Koxia and Permutation

Reve has two integers $ n $ and $ k $ . Let $ p $ be a permutation $ ^\dagger $ of length $ n $ . Let $ c $ be an array of length $ n - k + 1 $ such that $ $$$c_i = \max(p_i, \dots, p_{i+k-1}) + \min(p_i, \dots, p_{i+k-1}). $ $ Let the cost of the permutation $ p $ be the maximum element of $ c $ .

Koxia wants you to construct a permutation with the minimum possible cost.

$ ^\\dagger $ 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 consists of multiple test cases. The first line contains a single integer $ t $ ( $ 1 \leq t \leq 2000 $ ) — the number of test cases. The description of test cases follows. The first line of each test case contains two integers $ n $ and $ k $ ( $ 1 \leq k \leq n \leq 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, output $ n $ integers $ p_1,p_2,\dots,p_n $ , which is a permutation with minimal cost. If there is more than one permutation with minimal cost, you may output any of them.

In the first test case, - $ c_1 = \max(p_1,p_2,p_3) + \min(p_1,p_2,p_3) = 5 + 1 = 6 $ . - $ c_2 = \max(p_2,p_3,p_4) + \min(p_2,p_3,p_4) = 3 + 1 = 4 $ . - $ c_3 = \max(p_3,p_4,p_5) + \min(p_3,p_4,p_5) = 4 + 2 = 6 $ . Therefore, the cost is $ \max(6,4,6)=6 $ . It can be proven that this is the minimal cost.