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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;
import java.io.*;

public class Main {

	List<Integer>[] tree;
	int[] w;
	int INF = Integer.MAX_VALUE / 3;
	int[][] dp;

	int MAX = 6000;
	int[] buf = new int[MAX + 1];
	int[] buf2 = new int[MAX + 1];

	void dfs(int u) {
		for (int v : tree[u]) {
			dfs(v);
		}

		for (int col = 0; col < 2; col++) {
			Arrays.fill(buf, INF);
			buf[0] = 0;
			for (int v : tree[u]) {
				int val1 = dp[v][col];
				int val2 = dp[v][col ^ 1];
				Arrays.fill(buf2, INF);

				for (int i = 0; i <= MAX; i++) {
					// pairs (w[v], val2), (val1, w[v])
					if (i >= w[v]) {
						buf2[i] = Math.min(buf[i - w[v]] + val2, buf2[i]);
					}
					if (i >= val1) {
						buf2[i] = Math.min(buf[i - val1] + w[v], buf2[i]);
					}
				}
				System.arraycopy(buf2, 0, buf, 0, buf.length);
			}

			int min = INF;
			for (int i = 0; i <= w[u]; i++) {
				min = Math.min(min, buf[i]);
			}
			dp[u][col] = min;
		}
	}

	void solve() {
		int n = in.nextInt();
		tree = new List[n];
		for (int i = 0; i < n; i++) {
			tree[i] = new ArrayList<>();
		}
		for (int i = 1; i < n; i++) {
			tree[in.nextInt() - 1].add(i);
		}
		w = new int[n];
		for (int i = 0; i < n; i++) {
			w[i] = in.nextInt();
		}
		dp = new int[n][2];
		for (int[] i : dp) {
			Arrays.fill(i, INF);
		}
		dfs(0);
		if (dp[0][0] < INF || dp[0][1] < INF) {
			out.println("POSSIBLE");
		} else {
			out.println("IMPOSSIBLE");
		}
	}

	FastScanner in;
	PrintWriter out;

	void run() {
		in = new FastScanner();
		out = new PrintWriter(System.out);
		solve();
		out.close();
	}

	class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		public FastScanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		public FastScanner(String s) {
			try {
				br = new BufferedReader(new FileReader(s));
			} catch (FileNotFoundException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
			}
		}

		public String nextToken() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
				}
			}
			return st.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(nextToken());
		}

		public long nextLong() {
			return Long.parseLong(nextToken());
		}

		public double nextDouble() {
			return Double.parseDouble(nextToken());
		}
	}

	public static void main(String[] args) {
		new Main().run();
	}
}