#P1473C. No More Inversions
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ID: 5745
Type: RemoteJudge
2000ms
256MiB
Tried: 0
Accepted: 0
Difficulty: (None)
Uploaded By:
Hydro
Tags> No More Inversions
No submission language available for this problem.
Description
You 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 $t$).
The 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 $10^5$.
For 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.
Input
The 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 $10^5$.
Output
For 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.
Samples
4
1 1
2 2
3 2
4 3
1
1 2
2 1
1 3 2
Note
In 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.