Hongjun and the Tree 2

You are given a tree with $N$ vertices numbered from 0 to $N-1$.

Each vertex is painted white or black, and at least one vertex of each color is guaranteed to exist.

You can choose $k$ edges of the tree ($0 \le k < N$) and delete them. The vertices then split into $k+1$ sets. Count the ways to split the tree so that every resulting set contains exactly one black vertex. The value can grow very large, so print it modulo $10^9+7$.

The first line contains the number of vertices $N$ ($1 \le N \le 100000$).

The second line contains $N-1$ integers $p_0, p_1, \dots, p_{N-2}$ ($0 \le p_i \le i$). This means there is an edge between vertex $p_k$ and vertex $k+1$.

The third line contains $N$ integers $x_0, x_1, \dots, x_{N-1}$ giving the color of each vertex. If $x_i$ is 0, vertex $i$ is white; if it is 1, vertex $i$ is black.

Print the number of valid splittings modulo $10^9+7$ on one line.