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.*;
import java.util.*;

public class B implements Runnable{
	public static void main (String[] args) {new Thread(null, new B(), "_cf", 1 << 28).start();}

	int MOD = 1000000007;
	
	public void run() {
		FastScanner fs = new FastScanner();
		PrintWriter out = new PrintWriter(System.out);
		System.err.println("Go!");

		int n = fs.nextInt();
		ArrayList<Integer>[] adj = new ArrayList[n];
		for(int i = 0; i < n; i++) adj[i] = new ArrayList<>();
		for(int i = 1; i < n; i++) {
			int p = fs.nextInt();
			adj[p].add(i);
		}
		int[] colors = fs.nextIntArray(n);
		int[] queue = new int[n];
		int tail = 0;
		queue[tail++] = 0;
		for(int i = 0; i < tail; i++) {
			int u = queue[i];
			for(int v : adj[u]) queue[tail++] = v;
		}
		int[][] dp = new int[2][n];
		for(int i = n-1; i >= 0; i--) {
			int u = queue[i];
			dp[0][u] = 1; dp[1][u] = 0;
			for(int v : adj[u]) {
				dp[1][u] = mult(dp[0][v], dp[1][u]);
				dp[1][u] = add(dp[1][u], mult(dp[1][v], dp[0][u]));
				dp[0][u] = mult(dp[0][u], dp[0][v]);
			}
			if(colors[u] == 1) dp[1][u] = dp[0][u];
			else dp[0][u] = add(dp[0][u], dp[1][u]);
		}
		out.println(dp[1][0]);
		out.close();
	}
	
	int add(int a, int b) {
		return (a + b) % MOD;
	}
	
	int mult(long a, long b) {
		a *= b;
		return (int)(a%MOD);
	}

	class FastScanner {
		public int BS = 1<<16;
		public char NC = (char)0;
		byte[] buf = new byte[BS];
		int bId = 0, size = 0;
		char c = NC;
		double num = 1;
		BufferedInputStream in;

		public FastScanner() {
			in = new BufferedInputStream(System.in, BS);
		}

		public FastScanner(String s) throws FileNotFoundException {
			in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
		}

		public char nextChar(){
			while(bId==size) {
				try {
					size = in.read(buf);
				}catch(Exception e) {
					return NC;
				}                
				if(size==-1)return NC;
				bId=0;
			}
			return (char)buf[bId++];
		}

		public int nextInt() {
			return (int)nextLong();
		}

		public long nextLong() {
			num=1;
			boolean neg = false;
			if(c==NC)c=nextChar();
			for(;(c<'0' || c>'9'); c = nextChar()) {
				if(c=='-')neg=true;
			}
			long res = 0;
			for(; c>='0' && c <='9'; c=nextChar()) {
				res = (res<<3)+(res<<1)+c-'0';
				num*=10;
			}
			return neg?-res:res;
		}

		public double nextDouble() {
			double cur = nextLong();
			return c!='.' ? cur:cur+nextLong()/num;
		}

		public String next() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c>32) {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}

		public String nextLine() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c!='\n') {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}

		public boolean hasNext() {
			if(c>32)return true;
			while(true) {
				c=nextChar();
				if(c==NC)return false;
				else if(c>32)return true;
			}
		}
		
		public int[] nextIntArray(int n) {
			int[] res = new int[n];
			for(int i = 0; i < n; i++) res[i] = nextInt();
			return res;
		}
		
	}

}