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).
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,...,pn-2 (0≤pi≤i). Where pi means that there is an edge connecting vertex (i+1) of the tree and vertex pi. 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,...,xn-1 (xi is either 0 or 1). If xi is equal to 1, vertex i is colored black. Otherwise, vertex i is colored white.
Output a single integer − the number of ways to split the tree modulo 1000000007 (109+7).
3
0 0
0 1 1
2
6
0 1 1 0 4
1 1 0 0 1 0
1
10
0 1 2 1 4 4 4 0 8
0 0 0 1 0 1 1 0 0 1
27