A15693 | 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.

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.

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 $2 \cdot 10^{5}$ .