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.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {
    static class node {
        int color;
        List<node> childs;
        long blackNum = 0;
        long whiteNum = 0;

        node(int color) {
            this.color = color;
            childs = new ArrayList<>();
        }
    }

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        while (in.hasNext()) {
            int n = Integer.valueOf(in.nextLine());
            String[] nodes = in.nextLine().split(" ");//n-1
            String[] colors = in.nextLine().split(" ");//n
            node[] tree = new node[n];
            for (int i = 0; i < colors.length; i++) {
                tree[i] = new node(Integer.valueOf(colors[i]));
                if (Integer.valueOf(colors[i]) == 1) {
                    tree[i].blackNum = 1;
                } else {
                    tree[i].whiteNum= 1;
                }
            }
            for (int i = 0; i < nodes.length; i++) {
                tree[Integer.valueOf(nodes[i])].childs.add(tree[i + 1]);
            }
            getNum(tree[0]);
            System.out.println(tree[0].blackNum);
        }
    }

    static void getNum(node node) {
        for (node child : node.childs) {
            getNum(child);
            long bn = node.blackNum;
            long wn = node.whiteNum;
            node.blackNum = ((bn * child.blackNum) % 1000000007 + (bn * child.whiteNum)% 1000000007 + (wn * child.blackNum)% 1000000007)% 1000000007;
            node.whiteNum = ((wn * child.whiteNum)% 1000000007 + (wn * child.blackNum)% 1000000007)% 1000000007;
        }
    }
}

			    		     	  	       			  	