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.InputStreamReader;
import java.io.IOException;
import java.util.Arrays;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
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();
	}
}

class TaskB {
    private static final int MODULO = (int) 1e9 + 7;

    public void solve(int testNumber, InputReader in, PrintWriter out) {
        int n = in.nextInt();
        int[] firstChild = new int[n];
        int[] nextSibling = new int[n];
        Arrays.fill(firstChild, -1);
        for (int i = 1; i < n; ++i) {
            int parent = in.nextInt();
            nextSibling[i] = firstChild[parent];
            firstChild[parent] = i;
        }
        int[] color = new int[n];
        for (int i = 0; i < n; ++i) {
            color[i] = in.nextInt();
        }
        long[][] dp = new long[n][2];
        for (int at = n - 1; at >= 0; --at) {
            long[] ways = new long[2];
            ways[color[at]] = 1;
            for (int child = firstChild[at]; child != -1; child = nextSibling[child]) {
                long[] nways = new long[2];
                long[] cways = dp[child];
                nways[0] = (ways[0] * cways[1] + ways[0] * cways[0]) % MODULO;
                nways[1] = (ways[1] * cways[1] + ways[0] * cways[1] + ways[1] * cways[0]) % MODULO;
                ways = nways;
            }
            dp[at] = ways;
        }
        out.println(dp[0][1]);
    }
}

class InputReader {
    private BufferedReader reader;
    private 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());
    }

}

