Charmed by the Game

Description:

Input:

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^3$$$). Description of the test cases follows.

Each of the next $$$t$$$ lines describes one test case and contains two integers $$$a$$$ and $$$b$$$ ($$$0 \le a, b \le 10^5$$$; $$$a + b > 0$$$) — the number of games won by Alice and Borys, respectively.

It is guaranteed that the sum of $$$a + b$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output:

For each test case print two lines.

In the first line, print a single integer $$$m$$$ ($$$1 \le m \le a + b + 1$$$) — the number of values of $$$k$$$ such that exactly $$$k$$$ breaks could happen during the match.

In the second line, print $$$m$$$ distinct integers $$$k_1, k_2, \ldots, k_m$$$ ($$$0 \le k_1 < k_2 < \ldots < k_m \le a + b$$$) — the sought values of $$$k$$$ in increasing order.

Sample Input:

3
2 1
1 1
0 5

Sample Output:

4
0 1 2 3
2
0 2
2
2 3

Note:

In the first test case, any number of breaks between $$$0$$$ and $$$3$$$ could happen during the match:

• Alice holds serve, Borys holds serve, Alice holds serve: $$$0$$$ breaks;
• Borys holds serve, Alice holds serve, Alice breaks serve: $$$1$$$ break;
• Borys breaks serve, Alice breaks serve, Alice holds serve: $$$2$$$ breaks;
• Alice breaks serve, Borys breaks serve, Alice breaks serve: $$$3$$$ breaks.

In the second test case, the players could either both hold serves ($$$0$$$ breaks) or both break serves ($$$2$$$ breaks).

In the third test case, either $$$2$$$ or $$$3$$$ breaks could happen:

• Borys holds serve, Borys breaks serve, Borys holds serve, Borys breaks serve, Borys holds serve: $$$2$$$ breaks;
• Borys breaks serve, Borys holds serve, Borys breaks serve, Borys holds serve, Borys breaks serve: $$$3$$$ breaks.