CF1774H.Maximum Permutation

Ecrade bought a deck of cards numbered from $1$ to $n$. Let the value of a permutation $a$ of length $n$ be $\min\limits_{i = 1}^{n - k + 1}\ \sum\limits_{j = i}^{i + k - 1}a_j$.

Ecrade wants to find the most valuable one among all permutations of the cards. However, it seems a little difficult, so please help him!

Ecrade 购买了一副编号从 $1$ 到 $n$ 的扑克牌。定义一个长度为 $n$ 的排列 $a$ 的价值为 $\min\limits_{i = 1}^{n - k + 1}\ \sum\limits_{j = i}^{i + k - 1}a_j$。

Ecrade 希望在所有卡片的排列中找出价值最大的那个。然而，这似乎有点困难，所以请帮帮他！

The first line contains a single integer $t$ ($1 \leq t \leq 2 \cdot 10^4$) — the number of test cases. The description of test cases follows.

The only line of each test case contains two integers $n,k$ ($4 \leq k \lt n \leq 10^5$).

It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^6$.

第一行包含一个整数 $t$（$1 \leq t \leq 2 \cdot 10^4$）—— 表示测试用例的数量。随后是各测试用例的描述。

每个测试用例仅有一行，包含两个整数 $n$ 和 $k$（$4 \leq k \lt n \leq 10^5$）。

保证所有测试用例的 $n$ 之和不超过 $2 \cdot 10^6$。

For each test case, output the largest possible value in the first line. Then in the second line, print $n$ integers $a_1,a_2,\dots,a_n$ ($1 \le a_i \le n$, all $a_i$ are distinct) — the elements of the permutation that has the largest value.

If there are multiple such permutations, output any of them.

对于每个测试用例，在第一行输出可能的最大值。然后在第二行输出 $n$ 个整数 $a_1,a_2,\dots,a_n$（其中 $1 \le a_i \le n$，且所有 $a_i$ 互不相同）——即达到该最大值的排列的各个元素。

如果存在多个满足条件的排列，输出任意一个即可。

In the first test case, $[1,4,5,3,2]$ has a value of $13$. It can be shown that no permutations of length $5$ have a value greater than $13$ when $k = 4$.

In the second test case, $[4,2,5,7,8,3,1,6]$ has a value of $18$. It can be shown that no permutations of length $8$ have a value greater than $18$ when $k = 4$.

在第一个测试用例中，$[1,4,5,3,2]$ 的值为 $13$。可以证明：当 $k = 4$ 时，不存在长度为 $5$ 的排列其值大于 $13$。

在第二个测试用例中，$[4,2,5,7,8,3,1,6]$ 的值为 $18$。可以证明：当 $k = 4$ 时，不存在长度为 $8$ 的排列其值大于 $18$。