CF1793B.Fedya and Array

For his birthday recently Fedya was given an array $a$ of $n$ integers arranged in a circle, For each pair of neighboring numbers ($a_1$ and $a_2$, $a_2$ and $a_3$, $\ldots$, $a_{n - 1}$ and $a_n$, $a_n$ and $a_1$) the absolute difference between them is equal to $1$.

Let's call a local maximum an element, which is greater than both of its neighboring elements. Also call a local minimum an element, which is less than both of its neighboring elements. Note, that elements $a_1$ and $a_n$ are neighboring elements.

Unfortunately, Fedya lost an array, but he remembered in it the sum of local maximums $x$ and the sum of local minimums $y$.

Given $x$ and $y$, help Fedya find any matching array of minimum length.

最近，费佳生日时收到了一个由 $n$ 个整数组成的环形数组 $a$。对于每一对相邻元素（即 $a_1$ 与 $a_2$、$a_2$ 与 $a_3$、$\ldots$、$a_{n - 1}$ 与 $a_n$、$a_n$ 与 $a_1$），它们的绝对差值均为 $1$。

我们称一个局部最大值为严格大于其两个相邻元素的元素；类似地，称一个局部最小值为严格小于其两个相邻元素的元素。注意：$a_1$ 和 $a_n$ 是相邻元素。

不幸的是，费佳丢失了该数组，但他记得数组中所有局部最大值之和为 $x$，所有局部最小值之和为 $y$。

给定 $x$ 和 $y$，请帮助费佳构造出任意一个满足条件且长度最短的数组。

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 1000$). Description of the test cases follows.

Each line of each test case contain two integers $x$ and $y$ ($-10^{9} \le y \lt x \le 10^{9}$) — the sum of local maximums and the sum of local minimums, respectively.

每个测试包含多个测试用例。第一行包含测试用例的数量 $t$（$1 \le t \le 1000$）。随后是各测试用例的描述。

每个测试用例的每一行包含两个整数 $x$ 和 $y$（$-10^{9} \le y \lt x \le 10^{9}$），分别表示局部最大值之和与局部最小值之和。

For each test case, in the first line print one integer $n$ — the minimum length of matching arrays.

In the second line print $n$ integers $a_1, a_2, \ldots, a_n$ ($-10^{9} \leqslant a_i \leqslant 10^{9}$) — the array elements such that the the absolute difference between each pair of neighboring is equal to $1$.

If there are multiple solutions, print any of them.

It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^{5}$.

对于每个测试用例，在第一行输出一个整数 $n$ —— 满足条件的数组的最小长度。

在第二行输出 $n$ 个整数 $a_1, a_2, \ldots, a_n$（其中 $-10^{9} \leqslant a_i \leqslant 10^{9}$）—— 表示该数组的元素，使得每一对相邻元素的绝对差值均为 $1$。

若存在多种解，输出任意一种即可。

保证所有测试用例的 $n$ 值之和不超过 $2 \cdot 10^{5}$。

In the first test case, the local maximums are the numbers at $3, 7$ and $10$ positions, and the local minimums are the numbers at $1, 6$ and $8$ positions. $x = a_3 + a_7 + a_{10} = 2 + 0 + 1 = 3$, $y = a_1 + a_6 + a_8 = 0 + (-1) + (-1) = -2$.

In the second test case, the local maximums are the numbers at $2$ and $10$ positions, and the local minimums are the numbers at $1$ and $3$ positions. $x = a_2 + a_{10} = -1 + 5 = 4$, $y = a_1 + a_3 = -2 + (-2) = -4$.

In the third test case, the local maximums are the numbers at $1$ and $5$ positions, and the local minimums are the numbers at $3$ and $6$ positions.

在第一个测试用例中，局部最大值位于位置 $3$、$7$ 和 $10$ 处的数字，局部最小值位于位置 $1$、$6$ 和 $8$ 处的数字。$x = a_3 + a_7 + a_{10} = 2 + 0 + 1 = 3$，$y = a_1 + a_6 + a_8 = 0 + (-1) + (-1) = -2$。

在第二个测试用例中，局部最大值位于位置 $2$ 和 $10$ 处的数字，局部最小值位于位置 $1$ 和 $3$ 处的数字。$x = a_2 + a_{10} = -1 + 5 = 4$，$y = a_1 + a_3 = -2 + (-2) = -4$。

在第三个测试用例中，局部最大值位于位置 $1$ 和 $5$ 处的数字，局部最小值位于位置 $3$ 和 $6$ 处的数字。