Ksyusha and Chinchilla

Description:

Input:

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — number of testcases.

The first line of each testcase contains a single integer $$$n$$$ ($$$2 \le n \le 2 \cdot 10^5$$$) — the number of vertices in the tree.

The next $$$n - 1$$$ rows of each testcase contain integers $$$v_i$$$ and $$$u_i$$$ ($$$1 \le v_i, u_i \le n$$$) — the numbers of vertices that the $$$i$$$-th edge connects.

It is guaranteed that this set of edges forms a tree. It is also guaranteed that the sum of $$$n$$$ over all testcases does not exceed $$$2 \cdot 10^5$$$.

Output:

Print the answer for each testcase.

If the desired way to cut the tree does not exist, print $$$-1$$$.

Otherwise, print an integer $$$k$$$ — the number of edges to be cut. In the next line, print $$$k$$$ different integers $$$e_i$$$ ($$$1 \le e_i < n$$$) — numbers of the edges to be cut. If $$$k = 0$$$, print an empty string instead.

If there are several solutions, you can print any.

Sample Input:

4
9
1 2
4 3
7 9
5 4
4 6
3 2
8 7
1 7
6
1 2
1 3
4 3
1 5
6 1
6
1 2
3 2
3 4
4 5
6 5
5
1 3
5 3
5 2
3 4

Sample Output:

2
2 8 
-1
1
3 
-1

Sample Input:

4
2
1 2
3
1 2
3 1
6
1 2
3 1
3 4
3 5
6 1
9
2 6
6 9
9 1
9 7
1 8
7 3
8 5
4 7

Sample Output:

-1
0

1
2 
2
4 3 

Note:

The first testcase in first test.