human
I found an interesting problem on https://codeforces.com/problemset/problem/461/B:
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).

-----Input-----

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-----

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

-----Examples-----
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
27

I tried it in Python, but could not do it. Can you solve it?

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What is a Python program to find this number modulo 1000000007 (10^9 + 7)?
assistant
#Here is Python program to find this number modulo 1000000007 (10^9 + 7).

from collections import UserDict

class Tree(UserDict):
    def __init__(self, g):
        super().__init__()
        for name, value in enumerate(g, 1):
            self[value] = name

    def __setitem__(self, name, value):
        if name in self:
            if value is not None:
                self[name].add(value)
                self[value] = None
        else:
            if value is None:
                super().__setitem__(name, set())
            else:
                super().__setitem__(name, {value})
                self[value] = None

def __starting_point():
    n = int(input())

    tree = Tree(int(i) for i in input().split())
    colors = [int(i) for i in input().split()]
    t = [()] * n

    def dfs(v):
        stack = [v]
        visited = set()

        while stack:
            v = stack.pop()
            if v not in visited:
                visited.add(v)
                stack.append(v)
                stack.extend(tree[v])
            else:
                t[v] = (1, colors[v])
                for u in tree[v]:
                    t[v] = (
                        (t[v][0] * t[u][1] + t[v][0] * t[u][0] * (not colors[u])) % (10**9 + 7),
                        (t[v][1] * t[u][1] + t[v][0] * t[u][1] * (not colors[v])
                                           + t[v][1] * t[u][0] * (not colors[u])) % (10**9 + 7)
                    )

                
    dfs(0)

    print(t[0][1])


    



# Made By Mostafa_Khaled

__starting_point()