codeforces-461b Appleman and tree--tree DP problem __ Search timeout? D

the love story of the Apple Man and the tree

Apple Man and tree love story topic description-english Approximate question analysis-bare tree dp Count dp-State definition dp-State transfer Equation code-you group of hands don't always think about copying.

@ Topic Description @-english

Appleman has a tree with n vertices. Some of the vertices (at least one) are colored black and other vertices are 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 would split into (k + 1) parts. Note, which is a tree with colored vertices.
Now Appleman wonders, what are the number of sets splitting the tree in such a way this each resulting part would have exact Ly one black vertex? Find this number modulo 1000000007 (10^9 + 7).

Input
The 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, p0, ..., p1 (pn-2). Where Pi means that there is a 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 (xi are X1 0 or 1). If Xi is equal to 1, vertex I are colored black. Otherwise, vertex i is colored white.

Output
Output a single integer-the number of ways to split the modulo 1000000007 (10^9 + 7).

Some Example

Input
3
0 0
0 1 1
Output
2

Input
6
0 1 1 0 4
1 1 0 0 1 0
Output
1

Input
10
0 1 2 1 4 4 4 0 8
0 0 0 1 0 1 1 0 0 1
Output
@ roughly

Appleman has a tree containing n (2≤n≤10^5) vertices, some of which are black. Appleman have nothing to do, want to cut off a few edges, so that the remaining connected blocks each contains a black dot (obviously cut off the edge should be the number of black nodes-1). The vertex number is 0~n-1.
input n; input n-1 number, the first Number pi table vertex i and PI connectivity, and then input n number, in turn, the color of each vertex, 0 white 1 black.
Let you seek to meet the Appleman desire of the scheme of the number of modules 10^9 + 7. @ Analysis-Bare tree dp count @

There are trees, to the statistical scheme, as the title shows. @dp-Status definition @

Now to figure out how to define the state. As the picture shows a tree with a root, imagine dividing it into several connected blocks, which is the most special one. The is obviously the connected block that contains the root node. The contains a black dot in the connected block of the root node that has three sources: its subtree, its own, its father above "if it has a father". If it is more than its father, it can be handed over to its father recursively. If it is itself, then its subtree is either disconnected or self-reliant, or connected to the white-washing ego. If on its subtree, a Shang tree is to feed the parent node.
Then we define the two-dimensional state: dp[i][2] D p [i] [2] dp[i][2]
Dp[i][0]: After the subtree with I is cut off, the total number of connected blocks containing I that do not contain black dots d p [i] [0]: a son of the root of I When the tree is cut, the total number of connected blocks containing I without black dots dp[i][0]: The total number of solutions with no black spots in the connected block with I after cutting the edge of the subtree with I as root
Dp[i][1]: After the subtree with I is cut, the connected block containing I has a black dot