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.List;
import java.io.InputStreamReader;
import java.io.IOException;
import java.io.OutputStreamWriter;
import java.io.BufferedWriter;
import java.util.ArrayList;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Writer;
import java.util.StringTokenizer;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author Lokesh Khandelwal
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		OutputWriter out = new OutputWriter(outputStream);
		TaskB solver = new TaskB();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskB {
    long dp[][], a[], MOD = (int)1e9 + 7;
    List<Integer> edges[];
    int type[];
    public void solve(int testNumber, InputReader in, OutputWriter out) {
        int n = in.nextInt(), i;
        edges = new List[n];
        dp = new long[n][2];
        a = new long[2];
        type = new int[n];
        for(i=0;i<n;i++) {
            edges[i] = new ArrayList<Integer>();
        }
        for(i=1;i<n;i++) {
            int k = in.nextInt();
            edges[k].add(i);
        }
        for(i=0;i<n;i++) {
            type[i] = in.nextInt();
        }
        dfs(0);
        out.printLine(dp[0][1]);
    }
    public void dfs(int index) {
        dp[index][type[index]] = 1;
        dp[index][1 - type[index]] = 0;
        int v;
        for(int i=edges[index].size()-1;i>=0;i--) {
            v = edges[index].get(i);
            dfs(v);
            a[0] = dp[index][0];
            a[1] = dp[index][1];
            dp[index][0] = (a[0] * (dp[v][0] + dp[v][1])) % MOD;
            dp[index][1] = (a[1] * (dp[v][0] + dp[v][1]) + (a[0] * dp[v][1])) % MOD;
        }
    }
}

class InputReader
{
    BufferedReader in;
    StringTokenizer tokenizer=null;

    public InputReader(InputStream inputStream)
    {
        in=new BufferedReader(new InputStreamReader(inputStream));
    }
    public String next()
    {
        try{
            while (tokenizer==null||!tokenizer.hasMoreTokens())
            {
                tokenizer=new StringTokenizer(in.readLine());
            }
            return tokenizer.nextToken();
        }
        catch (IOException e)
        {
            return null;
        }
    }
    public int nextInt()
    {
        return Integer.parseInt(next());
    }
}

class OutputWriter {
	private final PrintWriter writer;

	public OutputWriter(OutputStream outputStream) {
		writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
	}

	public OutputWriter(Writer writer) {
		this.writer = new PrintWriter(writer);
	}

	public void print(Object...objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}

	public void printLine(Object...objects) {
		print(objects);
		writer.println();
	}

	public void close() {
		writer.close();
	}
}

