Appleman and Tree

### 题目描述 给你一棵有 $n$ 个节点的树，下标从 $0$ 开始。 第 $i$ 个节点可以为白色或黑色。 现在你可以从中删去若干条边，使得剩下的每个部分恰有一个黑色节点。 问有多少种符合条件的删边方法，答案对 $10^9+7$ 取模。 ### 输入格式 第一行一个整数 $n(1\leq n\leq 10^5)$，表示节点个数。 接下来一行 $n-1$ 个整数 $(p_0,p_1,\cdots,p_{n-2},0\leq p_i\leq i)$，表示树中有一条连接节点 $p_i$ 和节点 $i+1$ 的边。 接下来一行 $n$ 个整数 $(x_0,x_1,\cdots,x_{n-1},0\leq x_i\leq 1)$，若 $x_i$ 为 $1$，则节点 $i$ 为黑色，否则为白色。 ### 输出格式 第一行一个整数，表示符合条件的删边方法的方案数对 $10^9+7$ 取模后的值。

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 $ ( $ 10^{9}+7 $ ).

The first line contains an integer $ n $ ( $ 2<=n<=10^{5} $ ) — 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.

Output a single integer — the number of ways to split the tree modulo $ 1000000007 $ ( $ 10^{9}+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