E. Klever Permutationtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given two integers n and k (k \le n), where k is even.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 [0,1,2] is also not a permutation (as n=3, but 3 is not present in the array).Your task is to construct a k-level permutation of length n.A permutation is called k-level if, among all the sums of continuous segments of length k (of which there are exactly n - k + 1), any two sums differ by no more than 1.More formally, to determine if the permutation p is k-level, first construct an array s of length n - k + 1, where s_i=\sum_{j=i}^{i+k-1} p_j, i.e., the i-th element is equal to the sum of p_i, p_{i+1}, \dots, p_{i+k-1}.A permutation is called k-level if \max(s) - \min(s) \le 1.Find any k-level permutation of length n.InputThe first line of the input contains a single integer t (1 \le t \le 10^4) — the number of test cases. This is followed by the description of the test cases.The first and only line of each test case contains two integers n and k (2 \le k \le n \le 2 \cdot 10^5, k is even), where n is the length of the desired permutation.It is guaranteed that the sum of n for all test cases does not exceed 2 \cdot 10^5.OutputFor each test case, output any k-level permutation of length n.It is guaranteed that such a permutation always exists given the constraints.ExampleInput
52 23 210 413 47 4Output
2 1
1 3 2
1 8 4 10 2 7 5 9 3 6
4 10 1 13 5 9 2 12 6 8 3 11 7
1 6 3 7 2 5 4
NoteIn the second test case of the example:   p_1 + p_2 = 3 + 1 = 4;  p_2 + p_3 = 1 + 2 = 3.  The maximum among the sums is 4, and the minimum is 3.
52 23 210 413 47 4
2 1 1 3 2 1 8 4 10 2 7 5 9 3 6 4 10 1 13 5 9 2 12 6 8 3 11 7 1 6 3 7 2 5 4 
['constructive algorithms', 'math', 'two pointers', '*1400']