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.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author beginner1010
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskB solver = new TaskB();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskB {
        ArrayList<Integer>[] G;
        int[] color;
        int MOD = (int) 1e9 + 7;
        long[][] dp;

        long mod(long x) {
            x %= MOD;
            if (x < 0) x += MOD;
            return x;
        }

        void dfs(int node, int parent) {
            for (Integer children : G[node])
                if (children != parent) {
                    dfs(children, node);
                    long[] preDP = new long[2]; // refers to the previous children
                    preDP[0] = dp[node][0];
                    preDP[1] = dp[node][1];
                    dp[node][0] = mod(preDP[0] * (dp[children][0] + dp[children][1]));
                    dp[node][1] = mod(preDP[1] * (dp[children][1] + dp[children][0]) + preDP[0] * dp[children][1]);
                }

            return;
        }

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            G = new ArrayList[n];
            for (int i = 0; i < n; i++)
                G[i] = new ArrayList<Integer>();
            for (int i = 0; i < n - 1; i++) {
                int p = in.nextInt();
                G[i + 1].add(p);
                G[p].add(i + 1);
            }

            color = new int[n];
            dp = new long[n + 1][2];
            for (int i = 0; i < n; i++) {
                color[i] = in.nextInt();
                dp[i][color[i]] = 1;
            }

            dfs(0, -1);
            out.println(dp[0][1]);

        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

    }
}

