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.

Input

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.

Output

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 $$$2 \cdot 10^{5}$$$.

Note

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.

Fedya and Array

Examples