CF1470D.Strange Housing

Students of Winter Informatics School are going to live in a set of houses connected by underground passages. Teachers are also going to live in some of these houses, but they can not be accommodated randomly. For safety reasons, the following must hold:

• All passages between two houses will be closed, if there are no teachers in both of them. All other passages will stay open.
• It should be possible to travel between any two houses using the underground passages that are open.
• Teachers should not live in houses, directly connected by a passage.

Please help the organizers to choose the houses where teachers will live to satisfy the safety requirements or determine that it is impossible.

冬季信息学学校的学生将住在一组由地下通道连接的房屋中。教师也将住在其中一些房屋中，但不能随意安排教师的住宿。出于安全考虑，必须满足以下条件：

• 若两个房屋中均无教师，则它们之间的所有通道都将关闭；其余所有通道均保持开放。
• 应能仅通过开放的地下通道在任意两座房屋之间通行。
• 教师不得住在彼此直接由通道相连的房屋中。

请帮助组织者选择教师所住的房屋，以满足上述安全要求；若无法满足，则判定为不可能。

The first input line contains a single integer $t$ — the number of test cases ($1 \le t \le 10^5$).

Each test case starts with two integers $n$ and $m$ ($2 \le n \le 3 \cdot 10^5$, $0 \le m \le 3 \cdot 10^5$) — the number of houses and the number of passages.

Then $m$ lines follow, each of them contains two integers $u$ and $v$ ($1 \le u, v \le n$, $u \neq v$), describing a passage between the houses $u$ and $v$. It is guaranteed that there are no two passages connecting the same pair of houses.

The sum of values $n$ over all test cases does not exceed $3 \cdot 10^5$, and the sum of values $m$ over all test cases does not exceed $3 \cdot 10^5$.

第一行输入包含一个整数 $t$ —— 测试用例的数量（$1 \le t \le 10^5$）。

每个测试用例以两个整数 $n$ 和 $m$ 开始（$2 \le n \le 3 \cdot 10^5$，$0 \le m \le 3 \cdot 10^5$）—— 分别表示房屋数量和通道数量。

接下来是 $m$ 行，每行包含两个整数 $u$ 和 $v$（$1 \le u, v \le n$，$u \neq v$），描述连接房屋 $u$ 和 $v$ 的一条通道。保证不存在两条通道连接同一对房屋。

所有测试用例中 $n$ 的总和不超过 $3 \cdot 10^5$，所有测试用例中 $m$ 的总和也不超过 $3 \cdot 10^5$。

For each test case, if there is no way to choose the desired set of houses, output "NO". Otherwise, output "YES", then the total number of houses chosen, and then the indices of the chosen houses in arbitrary order.

对于每个测试用例，若不存在满足要求的房屋集合，则输出 “NO”。否则，输出 “YES”，然后输出所选房屋的总数，再输出所选房屋的下标（顺序任意）。

The picture below shows the second example test.

下图展示了第二个样例测试。