Depth of the Tree Node with Value k

A tree T has $n$ vertices and $n-1$ edges. The vertices are numbered from 0 to $n-1$, and vertex 0 is the root. The edges have no weights. Each vertex in T is assigned a distinct value. Print the depth of the vertex whose assigned value is $k$. The root has depth 0, and each child has a depth exactly 1 greater than its parent.

The first line contains the number of vertices $n$ and the integer $k$, separated by a space.

Each of the next $n-1$ lines describes one edge. Each line contains a parent vertex number $p$ and a child vertex number $c$, separated by a space.

The next line contains the values assigned to vertices 0 through $n-1$, separated by spaces. The $i$-th number is the value assigned to vertex $i-1$.

Print the depth of the vertex whose assigned value is $k$ on the first line.

• $2 \le n \le 100,000$
• $0 \le k \le n-1$
• $0 \le p, c \le n-1$, $p \ne c$
• The edges form a tree.
• $0 \le$ the value assigned to each vertex $\le n-1$
• The values assigned to the vertices are distinct integers.