CF1770B.Koxia and Permutation

普及/提高-

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题目描述

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 cost of the permutation $p$ be the maximum element of $c$ .

Koxia wants you to construct a permutation with the minimum possible cost.

^\\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).

输入格式

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 $2 \cdot 10^5$ .

输出格式

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.

输入输出样例

输入#1

输出#1

5 1 2 3 4
1 2 3 4 5
3 2 4 1 6 5

说明/提示

In the first test case,

$c_1 = \max(p_1,p_2,p_3) + \min(p_1,p_2,p_3) = 5 + 1 = 6$ .
$c_2 = \max(p_2,p_3,p_4) + \min(p_2,p_3,p_4) = 3 + 1 = 4$ .
$c_3 = \max(p_3,p_4,p_5) + \min(p_3,p_4,p_5) = 4 + 2 = 6$ .

Therefore, the cost is $\max(6,4,6)=6$ . It can be proven that this is the minimal cost.

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