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
	/*	/ ﾌﾌ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ム
		/ )\⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀  Y
		(⠀⠀| ( ͡° ͜ʖ ͡°）⠀⌒(⠀ ノ
		(⠀ ﾉ⌒ Y ⌒ヽ-く __／
		| _⠀｡ノ| ノ｡ |/
		(⠀ー '_人`ー ﾉ
		⠀|\ ￣ _人'彡ﾉ
		⠀ )\⠀⠀ ｡⠀⠀ /
		⠀⠀(\⠀ #⠀ /
		⠀/⠀⠀⠀/ὣ====================D-
		/⠀⠀⠀/⠀ \ \⠀⠀\
		( (⠀)⠀⠀⠀⠀ ) ).⠀)
		(⠀⠀)⠀⠀⠀⠀⠀( | /
		|⠀ /⠀⠀⠀⠀⠀⠀ | /
		[_] ⠀⠀⠀⠀⠀[___]                     */
	// Main Code at the Bottom
	import java.util.*;
	import java.lang.*;
	import java.io.*;
	import java.math.BigInteger; 
	public class Main {
		//Fast IO class
	    static class FastReader {
	        BufferedReader br; 
	        StringTokenizer st; 
	        public FastReader() {
	        	boolean env=System.getProperty("ONLINE_JUDGE") != null;
	        	if(!env) {
	        		try {
						br=new BufferedReader(new FileReader("src\\input.txt"));
					} catch (FileNotFoundException e) {
						e.printStackTrace();
					}
	        	}
	        	else br = new BufferedReader(new InputStreamReader(System.in)); 
	        } 
	        String next() {
	            while (st == null || !st.hasMoreElements()) {
	                try {
	                    st = new StringTokenizer(br.readLine()); 
	                } 
	                catch (IOException  e) {
	                    e.printStackTrace(); 
	                } 
	            } 
	            return st.nextToken(); 
	        } 
	        int nextInt() {
	            return Integer.parseInt(next()); 
	        } 
	        long nextLong() {
	            return Long.parseLong(next()); 
	        } 
	        double nextDouble() {
	            return Double.parseDouble(next()); 
	        } 
	        String nextLine() {
	            String str = ""; 
	            try {
	                str = br.readLine(); 
	            } 
	            catch (IOException e) {
	                e.printStackTrace(); 
	            } 
	            return str; 
	        } 
	    }     
	    static long MOD=1000000000+7;
	    //Euclidean Algorithm
	    static long gcd(long A,long B){
	    	return (B==0)?A:gcd(B,A%B);
	    }
	    //Modular Exponentiation
	    static long fastExpo(long x,long n){
	        if(n==0) return 1;
	        if((n&1)==0) return fastExpo((x*x)%MOD,n/2)%MOD;
	        return ((x%MOD)*fastExpo((x*x)%MOD,(n-1)/2))%MOD;
	    }
	    //Modular Inverse
	    static long inverse(long x) {
	    	return fastExpo(x,MOD-2);
	    }
	    //Prime Number Algorithm
	    static boolean isPrime(long n){
	        if(n<=1) return false;
	        if(n<=3) return true;
	        if(n%2==0 || n%3==0) return false;
	        for(int i=5;i*i<=n;i+=6) if(n%i==0 || n%(i+2)==0) return false;
	        return true;
	    }
	    //Reverse an array
	    static void reverse(int arr[],int l,int r){
	    	while(l<r) {
	    		int tmp=arr[l];
	    		arr[l++]=arr[r];
	    		arr[r--]=tmp;
	    	}
	    }
	    //Print array
	    static void print1d(int arr[]) {
	    	out.println(Arrays.toString(arr));
	    }
	    static void print2d(int arr[][]) {
	    	for(int a[]: arr) out.println(Arrays.toString(a));
	    }
	    // Pair
	    static class pair{
	    	int x,y;
	    	pair(int a,int b){
	    		this.x=a;
	    		this.y=b;
	    	}
	    	public boolean equals(Object obj) {
	    		if(obj == null || obj.getClass()!= this.getClass()) return false;
	            pair p = (pair) obj;
	            return (this.x==p.x && this.y==p.y);
	        }
	    	public int hashCode() {
	            return Objects.hash(x,y);
	        }
	    }
	    static FastReader sc=new FastReader();
	    static PrintWriter out=new PrintWriter(System.out);  
	    //Main function(The main code starts from here
	    static int V,color[];
	    static long dp[][];
	    static ArrayList<Integer> graph[];
	    static void init(int n){
	        V=n;
	        dp=new long[n][2];
	        color=new int[n];
	        graph=new ArrayList[V];
	        for(int i=0;i<V;i++) graph[i]=new ArrayList<>();
	    }
	    static void addEdge(int src,int dest){
	        graph[src].add(dest);
	        graph[dest].add(src);
	    }
	    static long add(long a,long b) {
	    	return (a%MOD+b%MOD)%MOD;
	    }
	    static long mult(long a,long b) {
	    	return ((a%MOD)*(b%MOD))%MOD;
	    }
	    static long div(long a,long b) {
	    	return ((a%MOD)*(inverse(b)%MOD))%MOD;
	    }
	    static void dfs(int s,int p) {
	    	if(color[s]==1) {
	    		dp[s][1]=1;
	    		for(Integer x: graph[s]) {
	    			if(x==p) continue;
	    			dfs(x,s);
	    			dp[s][1]=mult(dp[s][1],add(dp[x][0],dp[x][1]));
	    		}
	    	}
	    	else {
	    		dp[s][0]=1;
	    		for(Integer x: graph[s]) {
	    			if(x==p) continue;
	    			dfs(x,s);
	    			dp[s][0]=mult(dp[s][0],add(dp[x][0],dp[x][1]));
	    		}
	    		for(Integer x: graph[s]) {
	    			if(x==p) continue;
	    			dp[s][1]=add(dp[s][1],mult(dp[x][1],div(dp[s][0],add(dp[x][1],dp[x][0]))));
	    		}
	    	}
	    }
	    public static void main (String[] args) throws java.lang.Exception {
	    	int test;
	    	test=1;
	    	//test=sc.nextInt();
	    	while(test-->0){
	    		int n=sc.nextInt();
	    		init(n);
	    		for(int i=0;i<n-1;i++) addEdge(i+1,sc.nextInt());
	    		for(int i=0;i<n;i++) color[i]=sc.nextInt();
	    		dfs(0,-1);
	    		out.println(dp[0][1]%MOD);
	    	}
	        out.flush();
	        out.close();
	    }
	}