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

public class D462 {

    public static BufferedReader in;
    public static PrintWriter out;
    public static StringTokenizer tokenizer;

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        in = new BufferedReader(new InputStreamReader(inputStream), 32768);
        out = new PrintWriter(outputStream);
        solve();
        out.close();
    }

    public static final long MOD = 1000000007;
    public static ArrayList<Integer> adj[];
    public static int[] col;
    public static long[][] dp;

    public static void solve() {
        int n = nextInt();
        dp = new long[n + 1][2];
        adj = new ArrayList[n];
        for (int i = 0; i < n; i++) {
            adj[i] = new ArrayList<Integer>();
        }
        for (int i = 0; i < n - 1; i++) {
            int p = nextInt();
            adj[p].add(i + 1);
        }
        col = nextIntArray(n);
        dfs(0);
        out.println(dp[0][1]);
    }

    public static void dfs(int v) {
        dp[v][0] = 1;
        dp[v][1] = 0;
        for (int u : adj[v]) {
            dfs(u);
            dp[v][1] *= dp[u][0];
            dp[v][1] %= MOD;
            dp[v][1] += dp[v][0] * dp[u][1];
            dp[v][1] %= MOD;
            dp[v][0] *= dp[u][0];
            dp[v][0] %= MOD;
        }
        if (col[v] == 1) {
            dp[v][1] = dp[v][0];
            dp[v][1] %= MOD;
        } else {
            dp[v][0] += dp[v][1];
            dp[v][0] %= MOD;
        }
    }

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

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

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

    public static double nextDouble() {
        return Double.parseDouble(next());
    }

    public static int[] nextIntArray(int size) {
        int[] result = new int[size];
        for (int i = 0; i < size; i++) {
            result[i] = nextInt();
        }
        return result;
    }

    public static long[] nextLongArray(int size) {
        long[] result = new long[size];
        for (int i = 0; i < size; i++) {
            result[i] = nextLong();
        }
        return result;
    }
}
