C. No More Inversionstime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou have a sequence a with n elements 1, 2, 3, \dots, k - 1, k, k - 1, k - 2, \dots, k - (n - k) (k \le n < 2k).Let's call as inversion in a a pair of indices i < j such that a[i] > a[j].Suppose, you have some permutation p of size k and you build a sequence b of size n in the following manner: b[i] = p[a[i]].Your goal is to find such permutation p that the total number of inversions in b doesn't exceed the total number of inversions in a, and b is lexicographically maximum.Small reminder: the sequence of k integers is called a permutation if it contains all integers from 1 to k exactly once.Another small reminder: a sequence s is lexicographically smaller than another sequence t, if either s is a prefix of t, or for the first i such that s_i \ne t_i, s_i < t_i holds (in the first position that these sequences are different, s has smaller number than t).InputThe first line contains a single integer t (1 \le t \le 1000) — the number of test cases.The first and only line of each test case contains two integers n and k (k \le n < 2k; 1 \le k \le 10^5) — the length of the sequence a and its maximum.It's guaranteed that the total sum of k over test cases doesn't exceed 10^5.OutputFor each test case, print k integers — the permutation p which maximizes b lexicographically without increasing the total number of inversions.It can be proven that p exists and is unique.ExampleInput
4
1 1
2 2
3 2
4 3
Output
1 
1 2 
2 1 
1 3 2 
NoteIn the first test case, the sequence a = [1], there is only one permutation p = [1].In the second test case, the sequence a = [1, 2]. There is no inversion in a, so there is only one permutation p = [1, 2] which doesn't increase the number of inversions.In the third test case, a = [1, 2, 1] and has 1 inversion. If we use p = [2, 1], then b = [p[a[1]], p[a[2]], p[a[3]]] = [2, 1, 2] and also has 1 inversion.In the fourth test case, a = [1, 2, 3, 2], and since p = [1, 3, 2] then b = [1, 3, 2, 3]. Both a and b have 1 inversion and b is the lexicographically maximum.
4
1 1
2 2
3 2
4 3

1  1 2  2 1  1 3 2  
['constructive algorithms', 'math', '*1500']