B. Appleman and Tree 树状DP

B. Appleman and Tree

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

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 modulo1000000007 (10⁹ + 7).

Input

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 integersp₀, p₁, ..., 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 from0 to n - 1.

The third line contains the description of the colors of the vertices: n integers x₀, x₁, ..., x_n - 1 (x_i is either 0 or 1). Ifx_i is equal to1, vertex i is colored black. Otherwise, vertexi is colored white.

Output

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

Sample test(s)

Input

30 00 1 1

Output

2

Input

60 1 1 0 41 1 0 0 1 0

Output

1

Input

100 1 2 1 4 4 4 0 80 0 0 1 0 1 1 0 0 1

Output

27题意： 给一个树，节点只有黑色或者白色，求砍任意条边，把树分割成若干的只有一个黑色节点的小树 的方案数；思路： 树状DP； 一条边<v,u> 有四种状态： <1,1>, <1, 0> ,<0,1>, <0,0>用dp[i][0] 代表含节点i的子树不含黑色点的方案数；dp[i][1] : 含节点i的子数含了一个黑色节点的方案数；假设v 的父节点， u 为其一子节点；dp[v][1] = dp[v][1] (含黑色节点) * dp[u][1] (子含黑色节点）                  + dp[v][1] * dp[u][0] 【保留<v,u>边, 把v所在含黑色的子树 与 u所在不含黑色的子树连接起来构成新的子树可能数有： dp[v][1] * dp[u][0]】