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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;

// author : Yuuki_Asuna   

public class Tree {
	
	static List<List<Integer>> adj;
	
	static long[][] dp;
	static int[] col;
	
	public static void main(String[] args) throws IOException {
		
		//Scanner in = new Scanner(System.in);
		
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		
		int v = Integer.parseInt(in.readLine());
		
		String[] line = in.readLine().split("\\s+");
		
		adj = new ArrayList<>();
		
		for(int i=0; i<=v; i++) {
			adj.add(new ArrayList<>());
		}
		for(int i=0; i<line.length;  i++) {
			int u = Integer.parseInt(line[i]);
			adj.get(i+1).add(u);
			adj.get(u).add(i+1);
		}
		
		col = new int[v];
		line = in.readLine().split("\\s+");
		for(int i=0; i<line.length; i++) {
			col[i] = Integer.parseInt(line[i]);
		}
		
		dp = new long[v+1][2];
		dfs(0, -100);	
		
		System.out.println(dp[0][1]);
	}

	private static void dfs(int i, int par) {
		
		if(col[i] == 1) {
			dp[i][1] = 1;
		}
		else {
			dp[i][0] =1;
		}
		
		for(int n : adj.get(i)) {
			

			if(n == par) {
				continue;
			}
			
			dfs(n, i);
			
				dp[i][1] = (dp[i][1] * dp[n][1]  + dp[i][1]*dp[n][0] + dp[i][0]*dp[n][1]);
				dp[i][1] %= 1000000007;
				
				dp[i][0] = (dp[i][0] * dp[n][0] + dp[i][0]*dp[n][1]);
				
				dp[i][0] %= 1000000007;

		}
	}
	
}
		