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 {
    private static class Node{
        public List<Node> childs=new ArrayList<>();
        public int color=0;
        public long whiteNum=0;
        public long blackNum=0;
    }

    public static void dfs(Node node){
        long mod=1000000007;
        for (Node child : node.childs) {
            dfs(child);
            long old0=node.whiteNum, old1=node.blackNum;
            node.whiteNum=old0*(child.whiteNum+child.blackNum)%mod;
            node.blackNum=(old1*(child.whiteNum+child.blackNum)+old0*child.blackNum)%mod;
        }
    }

    public static void main(String[] args) {
        
        Scanner scanner =new Scanner(System.in);
        int n=scanner.nextInt();
        Node[] vertex=new Node[n];
        for (int i = 0; i < n; i++) {
            vertex[i]=new Node();
        }
        for (int i = 0; i < n - 1; i++) {
            int p=scanner.nextInt();
            vertex[p].childs.add(vertex[i+1]);
        }
        for (int i = 0; i < n; i++) {
            vertex[i].color=scanner.nextInt();
            vertex[i].blackNum=vertex[i].color;
            vertex[i].whiteNum=vertex[i].color^1;
        }
        dfs(vertex[0]);
        System.out.println(vertex[0].blackNum);
    }
}
 	   	 	  		 		   	 	  	 	  	