A14372 | $Charmed by the Game$

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内存限制256MB

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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.

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 $2 \cdot 10^5$ .

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.

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C++ 编辑器

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