P17535 [JAG 2026 Summer Camp #1] Sliding Puzzle on Tree

You are given a tree with $N$ vertices numbered $1$ through $N$. The $i$-th edge of the tree connects vertices $u_i$ and $v_i$. Initially, for each $i$ ($1\le i\le N$), vertex $i$ contains one stone if $A_i=1$ and no stone if $A_i=0$. You can repeatedly perform the following operation: - Select an unchosen edge with a stone on exactly one of its endpoints, and move that stone to the other endpoint. Determine whether you can perform the operation exactly $N-1$ times. If possible, output the order in which the edges are selected.

The input contains one or more test cases. The first line of the input contains an integer $T$ ($1\le T\le 10^5$), which is the number of test cases. The descriptions of the $T$ test cases follow, each in the following format. ```text N u_1 v_1 u_2 v_2 ... u_{N-1} v_{N-1} A_1 A_2 ... A_N ``` The first line contains an integer $N$ ($2\le N\le 2\times 10^5$) representing the number of vertices. For each $i$ ($1\le i\le N-1$), the $i$-th of the following $N-1$ lines contains two integers $u_i$ and $v_i$ ($1\le u_i,v_i\le N$) separated by a space, representing that the $i$-th edge connects vertices $u_i$ and $v_i$. It is guaranteed that the given graph is a tree. The last line contains $N$ integers $A_1,A_2,\ldots,A_N$ ($A_i\in\{0,1\}$) separated by spaces. $A_i$ represents whether a stone is initially placed on vertex $i$. The sum of $N$ over all test cases does not exceed $2\times 10^5$.

For each test case, print the answer as follows. If it is impossible to perform the operation exactly $N-1$ times, output `No` on a single line. If it is possible, output `Yes` on the first line, followed by the sequence of edges on the second line in the following format: ```text e_1 e_2 ... e_{N-1} ``` Here, $e_k$ ($1\le e_k\le N-1$) represents the index of the edge selected in the $k$-th operation. If there are multiple valid sequences, you can output any of them.