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
#include <bits/stdc++.h>
using namespace std;
const long long MOD = 1e9 + 7;
vector<int> G[100001];
long long dp[100001][2], p[100001];
void dfs(int v, int pre) {
  dp[v][0] = 1 - p[v];
  dp[v][1] = p[v];
  for (int i = 0; i < G[v].size(); i++) {
    int nxt = G[v][i];
    if (nxt == pre) continue;
    dfs(nxt, v);
    int tdp[2];
    tdp[0] = tdp[1] = 0;
    for (int i = 0; i < 2; i++) {
      for (int j = 0; j < 2; j++) {
        if (i == 0) {
          tdp[0] += (dp[v][i] * dp[nxt][j]) % MOD;
          tdp[0] %= MOD;
        }
        if (i == 1 || j == 1) {
          tdp[1] += (dp[v][i] * dp[nxt][j]) % MOD;
          tdp[1] %= MOD;
        }
      }
    }
    dp[v][1] = tdp[1];
    dp[v][0] = tdp[0];
  }
}
int main() {
  int n, t;
  scanf("%d", &n);
  for (int i = 1; i < n; i++) {
    scanf("%d", &t);
    G[t].push_back(i);
  }
  for (int i = 0; i < n; i++) scanf("%d", &p[i]);
  dfs(0, -1);
  printf("%lld\n", dp[0][1]);
  return 0;
}
