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 = 1000000007

n = int(input())
p = [int(x) for x in input().split()]
x = [int(x) for x in input().split()]

children = [[] for x in range(n)]

for i in range(1,n):
    children[p[i-1]].append(i)

#print(children)

count = [(0,0) for i in range(n)]
for i in reversed(range(n)):
    prod = 1
    for ch in children[i]:
        prod *= count[ch][0]+count[ch][1]
    if x[i]:
        count[i] = (0,prod % MOD)
    else:
        tot = 0
        for ch in children[i]:
            cur = count[ch][1]*prod // (count[ch][0]+count[ch][1])
            tot += cur
        count[i] = (prod % MOD, tot % MOD)

print(count[0][1])
