A13999 | No More Inversions

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

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.