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 \le k \lt 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 \le n \le 105) - the number of tree vertices.

The second line contains the description of the tree: n-1 integers p0,p1,...,pn-2 (0 \le pi \le 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).