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.util.*;

public class Solver {

    StringTokenizer st;
    BufferedReader in;
    PrintWriter out;

    public static void main(String[] args) throws NumberFormatException, IOException {
        Solver solver = new Solver();
        long time = System.currentTimeMillis();
        solver.open();
        solver.solve();
        //System.out.println("Spend time:" + (System.currentTimeMillis() - time));
        solver.close();
    }

    public void open() throws IOException {
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(new OutputStreamWriter(System.out));
        //in = new BufferedReader(new FileReader("input.txt"));
        //out = new PrintWriter(new FileWriter("output.txt"));
    }

    boolean hasMoreTokens() throws IOException {
        while (st == null || !st.hasMoreTokens()) {
            String line = in.readLine();
            if (line == null)
                return false;
            st = new StringTokenizer(line);
        }
        return true;
    }

    public String nextToken() throws IOException {
        while (st == null || !st.hasMoreTokens()) {
            String line = in.readLine();
            if (line == null)
                return null;
            st = new StringTokenizer(line);
        }
        return st.nextToken();
    }

    public int nextInt() throws NumberFormatException, IOException {
        return Integer.parseInt(nextToken());
    }

    public long nextLong() throws NumberFormatException, IOException {
        return Long.parseLong(nextToken());
    }

    public double nextDouble() throws NumberFormatException, IOException {
        return Double.parseDouble(nextToken());
    }

    List<Integer>[] tree;
    boolean[] black;

    public long[] dfs(int v) {
        long[] result = {1, 0};

        for (int to : tree[v]) {
            long[] child = dfs(to);
            result = new long[]{
                    result[0] * ((child[1] + child[0]) % MOD) % MOD,
                    (result[1] * ((child[0] + child[1]) % MOD) % MOD + result[0] * child[1] % MOD) % MOD
            };
        }

        return black[v] ? new long[]{0, result[0]} : result;
    }

    final long MOD = 1000000007L;

    public void solve() throws NumberFormatException, IOException {
        int n = nextInt();

        tree = new List[n];
        for (int i = 0; i < n; i++)
            tree[i] = new ArrayList<>();

        for (int i = 0; i < n - 1; i++) {
            tree[nextInt()].add(i + 1);
        }

        black = new boolean[n];

        for (int i = 0; i < n; i++)
            black[i] = nextInt() == 1;

        out.println(dfs(0)[1]);
    }

    public void close() {
        out.flush();
        out.close();
    }
}