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.util.Scanner;
import java.util.Vector;

public class Cf461B {
    static int MOD = 1000000007;
    int n;
    int[] pi;
    Vector<Vector<Integer>> child;
    boolean[] color;
    long[][] dp;
    public static void main(String[] args) {
        Cf461B cf = new Cf461B();
        System.out.println(cf.run());
    }
    public Cf461B() {
        Scanner sc = new Scanner(System.in);
        n = sc.nextInt();
        pi = new int[n];
        color = new boolean[n];
        child = new Vector<Vector<Integer>> ();
        for (int i = 0; i < n; ++i)
            child.add(new Vector<Integer>());
        for (int i = 1; i < n; ++i) {
            pi[i] = sc.nextInt();
            child.elementAt(pi[i]).add(i);
        }
        for (int i = 0; i < n; ++i)
            color[i] = sc.nextInt() == 1;
        dp = new long[n][2];
    }
    public long run() {
        for (int u = n - 1; u >= 0; --u) { // assume color white
            dp[u][0] = 1;
            dp[u][1] = 0;
            for (Integer v : child.elementAt(u)) {
                dp[u][1] *= dp[v][1] + dp[v][0]; // cut or no cut
                if (dp[u][1] >= MOD) dp[u][1] %= MOD;

                dp[u][1] += dp[u][0] * dp[v][1]; // conserve (u, v)
                if (dp[u][1] >= MOD) dp[u][1] %= MOD;

                dp[u][0] *= dp[v][1] + dp[v][0]; // cut or no cut
                if (dp[u][0] >= MOD) dp[u][0] %= MOD;
            }
            if (color[u]) { // fix for color black
                dp[u][1] = dp[u][0];
                dp[u][0] = 0;
            }
        }
        return dp[0][1];
    }
}
