A15636 | Koxia and Permutation

Reve has two integers $n$ and $k$ .

Let $p$ be a permutation $^\dagger$ of length $n$ . Let $c$ be an array of length $n - k + 1$ such that $$$$c_i = \max(p_i, \dots, p_{i+k-1}) + \min(p_i, \dots, p_{i+k-1}). $$ Let the <span class="tex-font-style-it">cost</span> of the permutation $p$ be the maximum element of $c$ .</p><p>Koxia wants you to construct a permutation with the minimum possible cost.</p><p> $^\\dagger$ A permutation of length $n$ is an array consisting of $n$ distinct integers from $1$ to $n$ in arbitrary order. For example, $\[2,3,1,5,4\]$ is a permutation, but $\[1,2,2\]$ is not a permutation ( $2$ appears twice in the array), and $\[1,3,4\]$ is also not a permutation ( $n=3$ but there is $4$$$ in the array).

Each test consists of multiple test cases. The first line contains a single integer $t$ ( $1 \leq t \leq 2000$ ) — the number of test cases. The description of test cases follows.

The first line of each test case contains two integers $n$ and $k$ ( $1 \leq k \leq n \leq 2 \cdot 10^5$ ).

It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$ .

For each test case, output $n$ integers $p_1,p_2,\dots,p_n$ , which is a permutation with minimal cost. If there is more than one permutation with minimal cost, you may output any of them.