Problem:
Score : 700 points

Problem Statement

We have a tree with N vertices. Vertex 1 is the root of the tree, and the parent of Vertex i (2 \leq i \leq N) is Vertex P_i.

To each vertex in the tree, Snuke will allocate a color, either black or white, and a non-negative integer weight.

Snuke has a favorite integer sequence, X_1, X_2, ..., X_N, so he wants to allocate colors and weights so that the following condition is satisfied for all v.

The total weight of the vertices with the same color as v among the vertices contained in the subtree whose root is v, is X_v.

Here, the subtree whose root is v is the tree consisting of Vertex v and all of its descendants.

Determine whether it is possible to allocate colors and weights in this way.

Constraints

1 \leq N \leq 1 000

1 \leq P_i \leq i - 1

0 \leq X_i \leq 5 000

Inputs

Input is given from Standard Input in the following format:

N
P_2 P_3 ... P_N
X_1 X_2 ... X_N

Outputs

If it is possible to allocate colors and weights to the vertices so that the condition is satisfied, print POSSIBLE; otherwise, print IMPOSSIBLE.

Sample Input 1

3
1 1
4 3 2

Sample Output 1

POSSIBLE

For example, the following allocation satisfies the condition:

Set the color of Vertex 1 to white and its weight to 2.

Set the color of Vertex 2 to black and its weight to 3.

Set the color of Vertex 3 to white and its weight to 2.

There are also other possible allocations.

Sample Input 2

3
1 2
1 2 3

Sample Output 2

IMPOSSIBLE

If the same color is allocated to Vertex 2 and Vertex 3, Vertex 2 cannot be allocated a non-negative weight.

If different colors are allocated to Vertex 2 and 3, no matter which color is allocated to Vertex 1, it cannot be allocated a non-negative weight.

Thus, there exists no allocation of colors and weights that satisfies the condition.

Sample Input 3

8
1 1 1 3 4 5 5
4 1 6 2 2 1 3 3

Sample Output 3

POSSIBLE

Sample Input 4

1

0

Sample Output 4

POSSIBLE

Solution in Java7 (OpenJDK 1.7.0) (judge verdict: Accepted)

import java.io.*;
import java.math.BigInteger;
import java.util.*;

public class Main
{
    static class Node{
        int b = 0;
        int w = 0;
        List<Integer> child;
    }
    static int subsetSum(int[] arr, int target){
        int n = arr.length;
        int m = target + 1;
        boolean[][] dp = new boolean[n][m];
        for (int i = 0; i < n; i++) {
            if (arr[i] > target) continue;
            dp[i][arr[i]] = true;
        }
        for (int i = 1; i < n; i++) {
            for (int j = 0; j < m; j++) {
                if (dp[i-1][j]){
                    dp[i][j] = true;
                    if (j + arr[i] <= target){
                        dp[i][j+arr[i]] = true;
                    }
                }
            }
        }
        for (int i = m-1; i >= 0;i--) {
            if (dp[n-1][i]){
                return i;
            }
        }
        return 0;
    }

    static Node[] nodes;
    static int[] X;
    public static void main(String[] args) throws FileNotFoundException {
        Scanner sc= new Scanner(System.in);
        int N = sc.nextInt();
        nodes = new Node[N];
        X = new int[N];
        for (int i = 0; i < N; i++) {
            nodes[i] = new Node();
            nodes[i].child = new ArrayList<>();
        }
        for (int i = 1; i < N; i++) {
            int par = sc.nextInt();
            nodes[par - 1].child.add(i);
        }
        for (int i = 0; i < N; i++) {
            X[i] = sc.nextInt();
        }
        System.out.println(recur(0) ? "POSSIBLE": "IMPOSSIBLE");
    }

    public static boolean recur(int nodeIdx){
        Node cur = nodes[nodeIdx];
        if (cur.child == null || cur.child.size() == 0){
            cur.b = 0; cur.w = X[nodeIdx];
            return true;
        }
        for (int i = 0; i < cur.child.size(); i++) {
            if (!recur(cur.child.get(i))) {
                return false;
            }
        }
        int b = 0, w = 0;
        int[] swap = new int[cur.child.size()];
        for (int i = 0; i < cur.child.size(); i++) {
            int black = nodes[cur.child.get(i)].b;
            int white = nodes[cur.child.get(i)].w;
            b += Math.min(white, black);
            w += Math.max(white, black);
            swap[i] = Math.max(white, black) - Math.min(white, black);
        }
        if (b > X[nodeIdx]) {
            return false;
        }
        int sww = subsetSum(swap, X[nodeIdx] - b);
        cur.b = X[nodeIdx];
        cur.w = w - sww;
        return true;
    }

}