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

/**
 *
 * @author Ryu
 */
import java.util.*;
import java.io.*;
public class ApplemanandTree {

    

    public static void main(String[] args) {
       // Scanner input = new Scanner(System.in);
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        Solve solver = new Solve();
        solver.solve(1, in, out);
        out.close();
    }
}


class Solve
{
    int MAXN = 100010;
    int MOD = (int)1e9 + 7;
    int Color[];
    long Dp [][];
    List < Integer > Edge[];

    public void solve(int testcase,InputReader in,OutputWriter out)
    {
        int i;
        int N = in.nextInt();
        Edge = new List[N];
        for (i = 0; i < N; i++) {
            Edge[i] = new ArrayList<Integer>();
        }
        for (i = 0; i < N - 1; i++) {
            int u = in.nextInt();
            Edge[u].add(i + 1);
        }
        Dp = new long[N][2];
        Color = new int[N];
        for (i = 0; i < N; i++) {
            Color[i] = in.nextInt();
        }
        dfs(0, -1);
        out.printLine(Dp[0][1]);
    }
    public Long PowMod(long N, long P) {
        if (P == 0) {
            return 1L;
        }
        Long Res = PowMod(N, P / 2);
        Res = (Res * Res) % MOD;
        if (P % 2 == 1) {
            return (Res * N) % MOD;
        }
        return Res;
    }

    public void dfs(int idx, int parent) {
        int i = 0;
        Long Res = 1L;
        for (i = 0; i < Edge[idx].size(); i++) {
            int v =  Edge[idx].get(i);
            if (v == parent) {
                continue;
            }
            dfs(v, idx);
            Res = (Res * (Dp[v][0] + Dp[v][1])) % MOD;
        }
        if (Color[idx] == 1) {
            Dp[idx][0] = 0;
            Dp[idx][1] = Res;
        } else {
            Dp[idx][0] = Res;
            Res = 0L;
            for (i = 0; i < Edge[idx].size(); i++) {
                int v = Edge[idx].get(i);
                if (v == parent) {
                    continue;
                }
                Res += Dp[v][1] * ((Dp[idx][0] * PowMod(Dp[v][0] + Dp[v][1], MOD - 2)%MOD));
                Res %= MOD;
            }
            Dp[idx][1] = Res;
        }

    }
}
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();
	}
}