A15606. 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!

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 $n,k$ ( $4 \leq k < n \leq 10^5$ ).

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

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.

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 $k = 4$ .