CF1793B.Fedya and Array

普及/提高-

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题目描述

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.

输入格式

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 $y$ ( $-10^{9} \le y < x \le 10^{9}$ ) — the sum of local maximums and the sum of local minimums, respectively.

输出格式

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 $2 \cdot 10^{5}$ .

输入输出样例

输入#1

输出#1

10
0 1 2 1 0 -1 0 -1 0 1
16
-2 -1 -2 -1 0 1 2 3 4 5 4 3 2 1 0 -1 
6
1 0 -1 0 1 0
16
2 3 2 1 0 -1 0 -1 0 -1 0 1 2 1 0 1

说明/提示

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.

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