P16394 [ECUSTPC 2026 Spring] Echo Form

:::epigraph Did you manage to construct the sequence? You managed to construct the sequence. :::

The Construction Kingdom is still chasing Little T…… For a sequence of length $n$, define its prefix $\max$ sequence $x$ as $x_i = \max\{a_j : 1 \le j \le i\}$, and its prefix $\min$ sequence $y$ as $y_i = \min\{a_j : 1 \le j \le i\}$. Given $n$ and $k$, please construct two sequences $a$ and $b$ of length $n$ that satisfy the following conditions. If no such two sequences exist, report that there is no solution: - $a$ and $b$ are permutations of $1$ to $n$. - $a$ and $b$ differ in at least one position, i.e., there exists $i$ such that $a_i \ne b_i$. - For either sequence among $a$ and $b$, let its prefix $\max$ sequence be $x$ and prefix $\min$ sequence be $y$. It must satisfy: $$ \sum_{i=1}^{n}(x_i - y_i) = k. $$

The first line contains an integer $T \ (1 \le T \le 10^5)$, denoting the number of testdata. Each testdata contains one line with two integers $n$ and $k \ (2 \le n \le 10^5, 0 \le k \le 10^{10})$, denoting the length of the sequence and the difference between the prefix $\max$ and prefix $\min$. It is guaranteed that $\sum n \le 3 \times 10^5$ over all testdata.

For each testdata, if there exist two sequences that satisfy the conditions, output two lines. The first line outputs $n$ integers $a_1, a_2, \dots, a_n$, representing the first sequence $a$ you constructed. The next line outputs $n$ integers $b_1, b_2, \dots, b_n$, representing the second sequence $b$. If no such two sequences exist, output one line containing a single integer $-1$. If there are multiple valid answers, you may output any one of them.

### Sample 1 Explanation For the 3rd testdata, we verify whether the second sequence, i.e. sequence $b$, satisfies the conditions: - $\{1, 2, 4, 5, 3\}$ is a permutation of $1$ to $5$, because each integer appears exactly once. - The second element is $a_2 = 3$, $b_2 = 2$, and $a_2 \ne b_2$. - Its prefix $\max$ sequence is $x = \{1, 2, 4, 5, 5\}$, and its prefix $\min$ sequence is $y = \{1, 1, 1, 1, 1\}$. Thus, $$ \sum_{i=1}^{n}(x_i - y_i) = (1 - 1) + (2 - 1) + (4 - 1) + (5 - 1) + (5 - 1) = 0 + 1 + 3 + 4 + 4 = 12 = k. $$ ### Hint A permutation of $1$ to $n$ is a sequence of length $n$ in which each integer from $1$ to $n$ appears exactly once. Translated by ChatGPT 5