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
/**
 * DA-IICT
 * Author : PARTH PATEL
 */
import java.io.*;
import java.math.*;
import java.util.*;

import static java.util.Arrays.fill;
import static java.lang.Math.*;
import static java.util.Arrays.sort;
import static java.util.Collections.sort;


public class B461 {

	public static int mod = 1000000007;
	static FasterScanner in = new FasterScanner();
	static PrintWriter out = new PrintWriter(System.out);
	static int n;
	static int[] black;
	static ArrayList<Integer>[] adjacencylist;
	static long[][] dp;
	public static void dfs(int vertex,int parent)
	{
		dp[vertex][1]=black[vertex];
		dp[vertex][0]=1-black[vertex];
		
		for(int u : adjacencylist[vertex])
		{
			if(u==parent)
				continue;
				
			dfs(u, vertex);
			long[] old=new long[2];
			old[0]=dp[vertex][0];
			old[1]=dp[vertex][1];
			dp[vertex][0]=dp[vertex][1]=0;
			//u is included in subtree of vertex
			dp[vertex][1]+=(old[0]*dp[u][1]);
			dp[vertex][1]%=mod;
			dp[vertex][1]+=(old[1]*dp[u][0]);
			dp[vertex][1]%=mod;
			dp[vertex][0]+=(old[0]*dp[u][0]);
			dp[vertex][0]%=mod;
			//u is not included in subtree of vertex
			dp[vertex][1]+=(old[1]*dp[u][1]);
			dp[vertex][1]%=mod;
			dp[vertex][0]+=(old[0]*dp[u][1]);
			dp[vertex][0]%=mod;
		}
	}
	public static void main(String[] args) {

		n=in.nextInt();
		black=new int[n+1];
		adjacencylist=new ArrayList[n+1];
		dp=new long[n+1][2];
		for(int i=0;i<=n;i++)
		{
			adjacencylist[i]=new ArrayList<>();
		}
		for(int i=0;i<n-1;i++)
		{
			int x=in.nextInt();
			adjacencylist[x].add(i+1);
			adjacencylist[i+1].add(x);
		}
		for(int i=0;i<n;i++)
		{
			black[i]=in.nextInt();
		}
		dfs(1, -1);
		out.println(dp[1][1]%mod);
		out.close();

	}

	public static long pow(long x, long n, long mod) {
		long res = 1;
		for (long p = x; n > 0; n >>= 1, p = (p * p) % mod) {
			if ((n & 1) != 0) {
				res = (res * p % mod);
			}
		}
		return res;
	}

	public static long gcd(long n1, long n2) {
		long r;
		while (n2 != 0) {
			r = n1 % n2;
			n1 = n2;
			n2 = r;
		}
		return n1;
	}

	public static long lcm(long n1, long n2) {
		long answer = (n1 * n2) / (gcd(n1, n2));
		return answer;
	}

	static class FasterScanner {
		private byte[] buf = new byte[1024];
		private int curChar;
		private int snumChars;

		public int read() {
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) {
				curChar = 0;
				try {
					snumChars = System.in.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (snumChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public String nextLine() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndOfLine(c));
			return res.toString();
		}

		public String nextString() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public long nextLong() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public int nextInt() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public int[] nextIntArray(int n) {
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextInt();
			}
			return arr;
		}

		public long[] nextLongArray(int n) {
			long[] arr = new long[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextLong();
			}
			return arr;
		}

		private boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		private boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}
	}

}
