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
/**
 * Created by Aminul on 8/14/2018.
 */

import java.io.*;
import java.util.*;
import static java.lang.Math.*;

public class CF461B {
    public static void main(String[] args)throws Exception {
        FastReader in = new FastReader(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int n = in.nextInt();
        dp = new long[2][n];
        color = new int[n];
        g = genList(n);
        for (int i = 1; i <= n-1; i++) {
            int u = in.nextInt(), v = i;
            g[u].add(v); g[v].add(u);
        }
        for (int i = 0; i < n; i++) {
            color[i] = in.nextInt();
        }

        int root = 0;
        dfs(root, -1);

        pw.println(dp[1][root]);

        pw.close();
    }

    static List<Integer> g[];
    static int color[];
    static long dp[][], mod = (long)1e9+7;

    static void dfs(int u, int p){
        dp[0][u] = 1;
        for(int v : g[u]){
            if(v == p) continue;
            dfs(v, u);
            dp[1][u] = (dp[0][u] * dp[1][v] + dp[1][u] * dp[0][v]) % mod;
            dp[0][u] = (dp[0][u] * dp[0][v]) % mod;
        }
        if(color[u] == 1) {
            dp[1][u] = dp[0][u];
        }
        else{
            dp[0][u] = (dp[0][u] + dp[1][u]) % mod;
        }
    }

    static <T>List<T>[] genList(int n){
        List<T> list[] = new List[n];
        for(int i = 0; i < n; i++) list[i] = new ArrayList<T>();
        return list;
    }

    static void debug(Object...obj) {
        System.err.println(Arrays.deepToString(obj));
    }

    static class FastReader {
        InputStream is;
        private byte[] inbuf = new byte[1024];
        private int lenbuf = 0, ptrbuf = 0;
        static final int ints[] = new int[128];

        public FastReader(InputStream is){
            for(int i='0';i<='9';i++) ints[i]=i-'0';
            this.is = is;
        }

        public int readByte(){
            if(lenbuf == -1)throw new InputMismatchException();
            if(ptrbuf >= lenbuf){
                ptrbuf = 0;
                try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
                if(lenbuf <= 0)return -1;
            }
            return inbuf[ptrbuf++];
        }

        public boolean isSpaceChar(int c) {
            return !(c >= 33 && c <= 126);
        }
        public int skip() {
            int b;
            while((b = readByte()) != -1 && isSpaceChar(b));
            return b;
        }

        public String next(){
            int b = skip();
            StringBuilder sb = new StringBuilder();
            while(!(isSpaceChar(b))){
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }

        public int nextInt(){
            int num = 0, b;
            boolean minus = false;
            while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
            if(b == '-'){
                minus = true;
                b = readByte();
            }

            while(true){
                if(b >= '0' && b <= '9'){
                    num = (num<<3) + (num<<1) + ints[b];
                }else{
                    return minus ? -num : num;
                }
                b = readByte();
            }
        }

        public long nextLong() {
            long num = 0;
            int b;
            boolean minus = false;
            while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
            if(b == '-'){
                minus = true;
                b = readByte();
            }

            while(true){
                if(b >= '0' && b <= '9'){
                    num = (num<<3) + (num<<1) + ints[b];
                }else{
                    return minus ? -num : num;
                }
                b = readByte();
            }
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }
       /* public char nextChar() {
            return (char)skip();
        }*/

        public char[] next(int n){
            char[] buf = new char[n];
            int b = skip(), p = 0;
            while(p < n && !(isSpaceChar(b))){
                buf[p++] = (char)b;
                b = readByte();
            }
            return n == p ? buf : Arrays.copyOf(buf, p);
        }

        /*private char buff[] = new char[1005];
        public char[] nextCharArray(){
            int b = skip(), p = 0;
            while(!(isSpaceChar(b))){
                buff[p++] = (char)b;
                b = readByte();
            }
            return Arrays.copyOf(buff, p);
        }*/
    }
}