CF1558A.Charmed by the Game

普及/提高-

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题目描述

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.

输入格式

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 $2 \cdot 10^5$ .

输出格式

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.

输入输出样例

输入#1
```
3
2 1
1 1
0 5
```
输出#1
```
4
0 1 2 3
2
0 2
2
2 3
```

说明/提示

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.

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