CF461B.Appleman and Tree

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).

Appleman 有一棵包含 $n$ 个顶点的树。其中部分顶点（至少一个）被染成黑色，其余顶点被染成白色。

考虑由 Appleman 的树中 $k$ 条边（$0 \leq k < n$）构成的一个集合。若 Appleman 将这些边从树中删除，则该树将分裂为 $k+1$ 个连通部分。注意，每个部分仍是一棵树，且其顶点具有颜色。

现在 Appleman 想知道：有多少种边集，使得删除这些边后，每个连通部分恰好包含一个黑点？请输出该数目对 $1000000007$（即 $10^9 + 7$）取模的结果。

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 _p_0, _p_1, ..., 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 _x_0, _x_1, ..., 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.

第一行包含一个整数 $n$（$2 \leq n \leq 10^5$）——树的顶点数量。

第二行包含树的描述：$n-1$ 个整数 $p_0, p_1, \dots, p_{n-2}$（$0 \leq p_i \leq i$）。其中 $p_i$ 表示树中顶点 $i+1$ 与顶点 $p_i$ 之间存在一条边。树的顶点编号为 $0$ 到 $n-1$。

第三行包含顶点颜色的描述：$n$ 个整数 $x_0, x_1, \dots, x_{n-1}$（每个 $x_i$ 为 $0$ 或 $1$）。若 $x_i = 1$，则顶点 $i$ 为黑色；否则顶点 $i$ 为白色。

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

输出一个整数——将树分割的方式数目对 $1000000007$（即 $10^9 + 7$）取模的结果。