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).

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 integers p0, p1, ..., pn - 2 (0 ≤ pi ≤ i). Where pi means that there is an 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, x1, ..., xn - 1 (xi is either 0 or 1). If xi 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 (109 + 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
mod=10**9+7
n=int(input())
edges=list(map(int,input().split()))
colored=list(map(int,input().split()))
childs=[[] for i in range(n)]

for i in range(1,n):
    childs[edges[i-1]].append(i)

dp = [[0,0] for i in range(n)]

for i in range(n-1,-1,-1):
    prod=1
    for child in childs[i]:
        prod*=sum(dp[child])
    if colored[i]:
        dp[i]=[0,prod%mod]
    else:
        sec=0
        for child in childs[i]:
            now=dp[child][1]*prod//sum(dp[child])
            sec+=now
        dp[i]=[prod%mod,sec%mod]


print(dp[0][1])
