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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.File;
import java.io.FileNotFoundException;
import java.util.ArrayList;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.BufferedReader;
import java.io.FileReader;
import java.io.InputStream;

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

    static class TaskD
    {
        private int V;
        private long[] color;
        private long[][] dp;
        private ArrayList<Integer>[] g;
        private final static long MOD = (int) 1e9 + 7;

        public void solve(int testNumber, FastScanner in, FastPrinter out)
        {
            V = in.nextInt();
            g = new ArrayList[V];
            color = new long[V];
            dp = new long[V][2];

            for (int i = 0; i < V; i++)
            {
                g[i] = new ArrayList<Integer>();
            }

            for (int i = 1; i < V; i++)
            {
                int from = i;
                int to = in.nextInt();
                g[from].add(to);
                g[to].add(from);
            }


            for (int i = 0; i < V; i++)
            {
                color[i] = in.nextLong();
            }

            dfs(0, -1);

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

        public void dfs(int v, int parent)
        {
            if (color[v] == 1)
            {
                dp[v][0] = 0;
                dp[v][1] = 1;
            } else
            {
                dp[v][0] = 1;
                dp[v][1] = 0;
            }

            for (int i = 0; i < g[v].size(); i++)
            {
                int u = g[v].get(i);
                if (u != parent)
                {
                    long value1 = dp[v][0];
                    long value2 = dp[v][1];
                    dp[v][0] = dp[v][1] = 0;
                    dfs(u, v);
                    //U is included with the subtree rooted at V//
                    dp[v][0] += (value1 * dp[u][0]) % MOD;
                    dp[v][0] %= MOD;

                    dp[v][1] += (value2 * dp[u][0]) % MOD;
                    dp[v][1] %= MOD;
                    dp[v][1] += (value1 * dp[u][1]) % MOD;
                    dp[v][1] %= MOD;

                    //U is not included with the subtree rooted at V//
                    dp[v][0] += (value1 * dp[u][1]) % MOD;
                    dp[v][0] %= MOD;
                    dp[v][1] += (value2 * dp[u][1]) % MOD;
                    dp[v][1] %= MOD;
                }
            }
        }

    }

    static class FastScanner
    {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(InputStream is)
        {
            br = new BufferedReader(new InputStreamReader(is));
        }

        public FastScanner(File f)
        {
            try
            {
                br = new BufferedReader(new FileReader(f));
            } catch (FileNotFoundException e)
            {
                e.printStackTrace();
            }
        }

        public String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                String s = null;
                try
                {
                    s = br.readLine();
                } catch (IOException e)
                {
                    e.printStackTrace();
                }
                if (s == null)
                    return null;
                st = new StringTokenizer(s);
            }
            return st.nextToken();
        }

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

        public long nextLong()
        {
            return Long.parseLong(next());
        }

    }

    static class FastPrinter extends PrintWriter
    {
        public FastPrinter(OutputStream out)
        {
            super(out);
        }

        public FastPrinter(Writer out)
        {
            super(out);
        }

    }
}

