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.PrintWriter;
import java.util.*;


public class CF263D {
	static Map<Integer, List<Integer>> tree;
	static long [][] dp;
	static int [] color;
	static final int mod = 1000000007;
	
	public static void main(String [] args) {
		Scanner input = new Scanner(System.in);
		
		int n = input.nextInt();
		
		tree = new HashMap<Integer, List<Integer>>();
		dp = new long[n][2];
		
		for (int i = 0; i < n-1; i++) {
			int pi = input.nextInt();
			List<Integer> piNbr = tree.get(pi);
			if (piNbr == null) {
				piNbr = new ArrayList<Integer>();
				tree.put(pi, piNbr);
			}
			piNbr.add(i + 1);
						
			List<Integer> childNbr = tree.get(i+1);
			if (childNbr == null) {
				childNbr = new ArrayList<Integer>();
				tree.put(i+1, childNbr);
			}
			childNbr.add(pi);
		}
		
		color = new int[n];
		
		for (int i = 0; i < n; i++) {
			color[i] = input.nextInt();
		}
		
		input.close();
		
		dfs(0, -1);
		
		PrintWriter out = new PrintWriter(System.out);
		
		out.println(dp[0][1] % mod);
		
		out.close();
	}
	
	public static void dfs(int vertex, int parent) {	
		long [] old = new long[2];
		
		dp[vertex][0] = 1 - color[vertex];
		dp[vertex][1] = color[vertex];
		
		List<Integer> nbr = tree.get(vertex);				
		for (Integer u : nbr) {
			if (u != parent) {
				dfs(u, vertex);
				
				old[0] = dp[vertex][0] % mod;
				old[1] = dp[vertex][1] % mod;
				
				dp[vertex][0] = 0;
				dp[vertex][1] = 0;
				
				// keep (vertex, u) edge
				dp[vertex][1] += old[1] * dp[u][0];
				dp[vertex][1] %= mod;
				dp[vertex][1] += old[0] * dp[u][1];
				dp[vertex][1] %= mod;
				dp[vertex][0] += old[0] * dp[u][0];
				dp[vertex][0] %= mod;
				
				// remove (vertex, u) edge
				dp[vertex][1] += old[1] * dp[u][1];
				dp[vertex][1] %= mod;
				dp[vertex][0] += old[0] * dp[u][1];
				dp[vertex][0] %= mod;
			}
		}
	}
}
