Appleman and Tree

2000ms

262144K

Description:

Appleman has a tree with n vertices. Some of the vertices (at least one) are colored black and other vertices are colored white.

Consider a set consisting of k (0 ≤ k < n) edges of Appleman's tree. If Appleman deletes these edges from the tree, then it will split into (k + 1) parts. Note, that each part will be a tree with colored vertices.

Now Appleman wonders, what is the number of sets splitting the tree in such a way that each resulting part will have exactly one black vertex? Find this number modulo 1000000007 (10⁹ + 7).

Input:

The first line contains an integer n (2 ≤ n ≤ 10⁵) — the number of tree vertices.

The second line contains the description of the tree: n - 1 integers p₀, p₁, ..., p_n - 2 (0 ≤ p_i ≤ i). Where p_i means that there is an edge connecting vertex (i + 1) of the tree and vertex p_i. Consider tree vertices are numbered from 0 to n - 1.

The third line contains the description of the colors of the vertices: n integers x₀, x₁, ..., x_n - 1 (x_i is either 0 or 1). If x_i is equal to 1, vertex i is colored black. Otherwise, vertex i is colored white.

Output:

Output a single integer — the number of ways to split the tree modulo 1000000007 (10⁹ + 7).

Sample Input:

3
0 0
0 1 1

Sample Output:

Sample Input:

6
0 1 1 0 4
1 1 0 0 1 0

Sample Output:

Sample Input:

10
0 1 2 1 4 4 4 0 8
0 0 0 1 0 1 1 0 0 1

Sample Output:

Informação

Provedor Codeforces

Código CF461B