A13207. Modernization of Treeland

The first line contains an integer $t$ ( $1 \le t \le 10^4$ ) — the number of test cases in the input. This is followed by the test cases themselves.

Each test case begins with a line that contains two integers $n$ and $k$ ( $2 \le n \le 3 \cdot 10^5$ , $1 \le k \le n$ ) — the number of cities in Treeland and the number of "dead-end" cities required in the subset $S$ .

This is followed by $n-1$ lines with road descriptions. Each road is given by two integers $x$ and $y$ ( $1 \le x, y \le n$ ; $x \ne y$ ) — the numbers of the cities that are connected by this road. It is guaranteed that from every city you can reach any other, moving only by the roads.

The sum of the values of $n$ for all test cases in the input does not exceed $3 \cdot 10^5$ .

For each test case print Yes or No (in any case, upper or lower), depending on whether the answer exists or not. If the answer exists, then print an integer $m$ ( $1 \le m \le n$ ) — the number of cities in the found subset. Then print $m$ different numbers from $1$ to $n$ — the numbers of the cities in the found subset. City numbers can be printed in any order. If there are several answers, print any of them.

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