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).

输入描述:

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.

输出描述:

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