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.io.*;
import java.math.*;
import java.util.*;

public class Main {
    final static long MOD = (int)1e9 + 7;

    public void run() throws IOException {
        int n = reader.nextInt();
        int[] parent = new int[n];
        for (int i = 1; i < n; ++ i) {
            parent[i] = reader.nextInt();
        }
        long[][] ways = new long[n][2];
        for (int i = 0; i < n; ++ i) {
            ways[i][reader.nextInt()] = 1;
        }
        for (int u = n - 1; u >= 1; -- u) {
            int p = parent[u];
            ways[p] = new long[]{(ways[p][0] * ways[u][0] % MOD + ways[p][0] * ways[u][1] % MOD) % MOD,
                                 (ways[p][0] * ways[u][1] % MOD + ways[p][1] * ways[u][0] % MOD + ways[p][1] * ways[u][1] % MOD) % MOD};
        }
        writer.println(ways[0][1]);
        writer.close();
    }

    Main() {
        reader = new InputReader(System.in);
        writer = new PrintWriter(System.out);
    }

    public static void main(String[] args) throws IOException {
        new Main().run();
    }

    private void debug(Object...os) {
        System.err.println(Arrays.deepToString(os));
    }

    private InputReader reader;
    private PrintWriter writer;
}

class InputReader {
    InputReader(InputStream in) {
        reader    = new BufferedReader(new InputStreamReader(in));
        tokenizer = new StringTokenizer("");
    }

    public String next() throws IOException {
        while (!tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }

    public Integer nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    private BufferedReader  reader;
    private StringTokenizer tokenizer;
}
