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
import java.util.*;
import java.io.*;
public class Main{
    static PrintWriter out;
    static InputReader in;
    public static void main(String args[]){
        out = new PrintWriter(System.out);
        in = new InputReader();
        new Main();
        out.flush(); out.close();
    }   
    Main(){
        solve();
    }
    final int mod = (int)(1e9) + 7;
    void solve(){
        int n = in.nextInt();
        int p[] = new int[n];
        for(int i = 1; i < n; i++)p[i] = in.nextInt();
        int v[] = new int[n];
        for(int i = 0; i < n; i++)v[i] = in.nextInt();
        boolean visit[] = new boolean[n];
        long dp[][] = new long[n][2];
        for(int i = n - 1; i >= 0; i--){
            if(!visit[i]){
                dp[i][v[i]] = 1;
            }
            if(i == 0)break;
            long vw = dp[i][0], vb = dp[i][1];
            long vwb = (vw + vb) % mod;
            int pa = p[i];
            if(!visit[pa]){
                dp[pa][0] = v[pa] == 1 ? 0 : vwb; dp[pa][1] = v[pa] == 1 ? vwb : vb;
                visit[pa] = true;
            }else{
                dp[pa][1] = (dp[pa][0] * vb % mod + dp[pa][1] * vwb % mod) % mod;
                dp[pa][0] = dp[pa][0] * vwb % mod; 
            }
            // System.out.println(dp[i][0] + " " + dp[i][1]);
        }
        out.print(dp[0][1]);
    }
    public static class InputReader{
        BufferedReader br;
        StringTokenizer st;
        InputReader(){
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        public int nextInt(){
            return Integer.parseInt(next());
        }
        public long nextLong(){
            return Long.parseLong(next());
        }
        public double nextDouble(){
            return Double.parseDouble(next());
        }
        public String next(){
            while(st == null || !st.hasMoreTokens()){
                try{
                    st = new StringTokenizer(br.readLine());
                }catch(IOException e){}
            }
            return st.nextToken();
        }
    }
}
        