CF1473C.No More Inversions

You have a sequence $a$ with $n$ elements $1, 2, 3, \dots, k - 1, k, k - 1, k - 2, \dots, k - (n - k)$ ($k \le n \lt 2k$).

Let's call as inversion in $a$ a pair of indices $i \lt j$ such that $a[i] \gt a[j]$.

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 $s_i \ne t_i$, $s_i \lt t_i$ holds (in the first position that these sequences are different, $s$ has smaller number than $t$).

你有一个长度为 $n$ 的序列 $a$，其元素为 $1, 2, 3, \dots, k - 1, k, k - 1, k - 2, \dots, k - (n - k)$（其中 $k \le n < 2k$）。

我们称 $a$ 中的一个逆序对为满足 $i < j$ 且 $a[i] > a[j]$ 的下标对 $(i, j)$。

假设你有一个大小为 $k$ 的排列 $p$，并按如下方式构造一个长度为 $n$ 的序列 $b$：$b[i] = p[a[i]]$。

你的目标是找出一个排列 $p$，使得 $b$ 中的逆序对总数不超过 $a$ 中的逆序对总数，且 $b$ 在字典序上尽可能大。

小提示：若一个包含 $k$ 个整数的序列恰好包含从 $1$ 到 $k$ 的每个整数一次，则称其为一个排列。

另一个小提示：若序列 $s$ 比序列 $t$ 字典序更小，则满足以下条件之一：$s$ 是 $t$ 的前缀；或存在第一个下标 $i$ 使得 $s_i \ne t_i$，且 $s_i < t_i$（即在两序列首次出现差异的位置上，$s$ 的对应元素小于 $t$ 的对应元素）。

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 $k$ ($k \le n \lt 2k$; $1 \le k \le 10^5$) — the length of the sequence $a$ and its maximum.

It's guaranteed that the total sum of $k$ over test cases doesn't exceed $10^5$.

第一行包含一个整数 $t$（$1 \le t \le 1000$）—— 测试用例的数量。

每个测试用例的第一行（也是唯一一行）包含两个整数 $n$ 和 $k$（$k \le n \lt 2k$；$1 \le k \le 10^5$）—— 序列 $a$ 的长度及其最大值。

保证所有测试用例中 $k$ 的总和不超过 $10^5$。

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.

对于每个测试用例，输出 $k$ 个整数——即在不增加总逆序对数的前提下，使得序列 $b$ 的字典序最大的排列 $p$。

可以证明，这样的排列 $p$ 存在且唯一。

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.

在第一个测试用例中，序列 $a = [1]$，仅存在一个排列 $p = [1]$。

在第二个测试用例中，序列 $a = [1, 2]$。$a$ 中不存在逆序对，因此仅存在一个排列 $p = [1, 2]$，它不会使逆序对数量增加。

在第三个测试用例中，$a = [1, 2, 1]$，包含 $1$ 个逆序对。若取 $p = [2, 1]$，则 $b = [p[a[1]], p[a[2]], p[a[3]]] = [2, 1, 2]$，同样包含 $1$ 个逆序对。

在第四个测试用例中，$a = [1, 2, 3, 2]$，取 $p = [1, 3, 2]$，则 $b = [1, 3, 2, 3]$。$a$ 和 $b$ 均恰好有 $1$ 个逆序对，且 $b$ 是字典序最大的序列。