CF1558A.Charmed by the Game

Alice and Borys are playing tennis.

A tennis match consists of games. In each game, one of the players is serving and the other one is receiving.

Players serve in turns: after a game where Alice is serving follows a game where Borys is serving, and vice versa.

Each game ends with a victory of one of the players. If a game is won by the serving player, it's said that this player holds serve. If a game is won by the receiving player, it's said that this player breaks serve.

It is known that Alice won $a$ games and Borys won $b$ games during the match. It is unknown who served first and who won which games.

Find all values of $k$ such that exactly $k$ breaks could happen during the match between Alice and Borys in total.

爱丽丝和鲍里斯正在打网球。

一场网球比赛由若干局组成。在每一局中，其中一名选手发球，另一名选手接发球。

选手轮流发球：若一局由爱丽丝发球，则下一局由鲍里斯发球；反之亦然。

每局以其中一名选手获胜结束。若发球方赢得该局，则称其“保发”；若接发方赢得该局，则称其“破发”。

已知整场比赛中爱丽丝赢了 $a$ 局，鲍里斯赢了 $b$ 局。但谁先发球、以及每局具体由谁获胜均未知。

求所有可能的整数 $k$，使得爱丽丝与鲍里斯之间的这场比赛中，总共恰好发生了 $k$ 次破发。

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 $b$ ($0 \le a, b \le 10^5$; $a + b \gt 0$) — 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 $2 \cdot 10^5$.

每个测试包含多个测试用例。第一行包含测试用例的数量 $t$（$1 \le t \le 10^3$）。随后是测试用例的描述。

接下来的 $t$ 行中，每行描述一个测试用例，包含两个整数 $a$ 和 $b$（$0 \le a, b \le 10^5$；$a + b \gt 0$），分别表示 Alice 和 Borys 获胜的游戏局数。

保证所有测试用例中 $a + b$ 的总和不超过 $2 \cdot 10^5$。

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 $k_1, k_2, \ldots, k_m$ ($0 \le k_1 \lt k_2 \lt \ldots \lt k_m \le a + b$) — the sought values of $k$ in increasing order.

对每个测试用例，输出两行。

第一行，输出一个整数 $m$（$1 \le m \le a + b + 1$）—— 表示在比赛中恰好发生 $k$ 次破发的 $k$ 的取值个数。

第二行，输出 $m$ 个互不相同的整数 $k_1, k_2, \ldots, k_m$（$0 \le k_1 \lt k_2 \lt \ldots \lt k_m \le a + b$）—— 即所求的 $k$ 值，按升序排列。

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.

在第一个测试用例中，比赛过程中可能发生 $0$ 到 $3$ 次破发：

• 爱丽丝保发，鲍里斯保发，爱丽丝保发：$0$ 次破发；
• 鲍里斯保发，爱丽丝保发，爱丽丝破发：$1$ 次破发；
• 鲍里斯破发，爱丽丝破发，爱丽丝保发：$2$ 次破发；
• 爱丽丝破发，鲍里斯破发，爱丽丝破发：$3$ 次破发。

在第二个测试用例中，两名选手可能均保发（$0$ 次破发），也可能均破发（$2$ 次破发）。

在第三个测试用例中，可能发生 $2$ 次或 $3$ 次破发：

• 鲍里斯保发，鲍里斯破发，鲍里斯保发，鲍里斯破发，鲍里斯保发：$2$ 次破发；
• 鲍里斯破发，鲍里斯保发，鲍里斯破发，鲍里斯保发，鲍里斯破发：$3$ 次破发。