P13941 [EC Final 2019] Fire

$\textit{Pang}$ lives on a tree with $n$ vertices. The vertices are labelled as $1,2,\ldots, n$ and $\textit{Pang}$ is in vertex $1$. Each vertex has a temperature. On the morning of each day after day 0, the temperature of each vertex decreases by $1$. The temperature doesn't decrease on day 0. On the afternoon of each day, $\textit{Pang}$ can travel to an adjacent vertex, provided that he is at a vertex with positive temperature and his destination vertex has a non-negative temperature. On the evening of each day, if the temperature is higher than or equal to $0$, $\textit{Pang}$ can cast magic which increases the temperature of the vertex he is in by $k$. For each pair of adjacent vertices $a$ and $b$, $\textit{Pang}$ can travel from vertex $a$ to vertex $b$ at most once (and from $b$ to $a$ at most once). He can choose not to travel and stay in the current vertex. $\textit{Pang}$ wants to cast his magic on each vertex exactly once. He also tries to stay at vertex $1$ as long as possible, before traveling to any other city. Given the temperature of each vertex right before the morning of the day $1$, on which day must $\textit{Pang}$ prepare for departing? If $\textit{Pang}$ prepares on day $i$, he can cast his magic on that day and will make his first move on day $i+1$. If he cannot cast his magic on each vertex exactly once even if he prepares for departing on the day $0$, output $-1$.

The first line contains two integers $n$ and $k$ ($2\le n\le 100000, 0\le k\le 1000000000$). Each of the next $n-1$ lines contains two integers $x$ and $y$, indicating an edge between vertices $x$ and $y$ ($1\le x, y\le n$). The $(n+1)$-th line contains $n$ integers $a_1,a_2,\ldots,a_n$ --- the temperature of vertex $i$ right before the morning of day $1$ ($0\le a_i\le 1000000000$). It's guaranteed that the input is a tree structure.

If he cannot cast his magic on each vertex exactly once, output $-1$. Otherwise, output a single integer $x$ --- he must prepare for departing from vertex $1$ on day $x$. Day $1$ is the day after day $0$, and so on.