Koxia and Permutation

1000ms

262144K

Description:

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).

Input:

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 $$$2 \cdot 10^5$$$.

Output:

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.

Sample Input:

Sample Output:

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

Note:

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.

Informação

Provedor Codeforces

Código CF1770B