A16000. Tree Weights

You are given a tree with $n$ nodes labelled $1,2,\dots,n$ . The $i$ -th edge connects nodes $u_i$ and $v_i$ and has an unknown positive integer weight $w_i$ . To help you figure out these weights, you are also given the distance $d_i$ between the nodes $i$ and $i+1$ for all $1 \le i \le n-1$ (the sum of the weights of the edges on the simple path between the nodes $i$ and $i+1$ in the tree).

Find the weight of each edge. If there are multiple solutions, print any of them. If there are no weights $w_i$ consistent with the information, print a single integer $-1$ .

The first line contains a single integer $n$ ( $2 \le n \le 10^5$ ).

The $i$ -th of the next $n-1$ lines contains two integers $u_i$ and $v_i$ ( $1 \le u_i,v_i \le n$ , $u_i \ne v_i$ ).

The last line contains $n-1$ integers $d_1,\dots,d_{n-1}$ ( $1 \le d_i \le 10^{12}$ ).

It is guaranteed that the given edges form a tree.

If there is no solution, print a single integer $-1$ . Otherwise, output $n-1$ lines containing the weights $w_1,\dots,w_{n-1}$ .

If there are multiple solutions, print any of them.

In the first sample, the tree is as follows:

In the second sample, note that $w_2$ is not allowed to be $0$ because it must be a positive integer, so there is no solution.

In the third sample, the tree is as follows: