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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

//#pragma warning disable
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;
using System;
using System.Numerics;
using System.Threading.Tasks;
using static System.Math;
using static System.Console;
class Z { static void Main() => new K(); }
class K
{
	int F() => int.Parse(ReadLine());
	long FL() => long.Parse(ReadLine());
	int[] G() => ReadLine().Split(new char[] { ' ', '\t' }, StringSplitOptions.RemoveEmptyEntries).Select(int.Parse).ToArray();
	long[] GL() => ReadLine().Split(new char[] { ' ', '\t' }, StringSplitOptions.RemoveEmptyEntries).Select(long.Parse).ToArray();
	public const int MOD = 1000000007;
	public K()
	{
		SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
		Solve();
		Out.Flush();
	}
	int N;
	int[] P, X, Y;
	List<int>[] child;
	void Solve()
	{
		N = F();
		P = new int[N];
		P[0] = -1;
		X = G();
		child = new List<int>[N];
		for (var i = 0; i < N; i++) child[i] = new List<int>();
		for (var i = 0; i < N - 1; i++)
		{
			P[i + 1] = X[i] - 1;
			child[i + 1].Add(P[i + 1]);
			child[P[i + 1]].Add(i + 1);
		}
		X = G();
		Y = new int[N];
		WriteLine(DFS(0, -1) >= 0 ? "POSSIBLE" : "IMPOSSIBLE");
	}
	int DFS(int v, int p)
	{
		var x = new List<int>();
		var y = new List<int>();
		foreach (var c in child[v])
			if (c != p)
			{
				x.Add(X[c]);
				var t = DFS(c, v);
				if (t < 0) return Y[v] = -1;
				y.Add(t);
			}
		var d = x.Count;
		if (d == 0) return Y[v] = 0;
		var s = 0;
		for (var i = 0; i < d; i++) s += Min(x[i], y[i]);
		if (s > X[v]) return Y[v] = -1;
		var m = new int[X[v] + 1];
		for (var i = 1; i <= X[v]; i++) m[i] = MOD;
		for (var i = 0; i < d; i++)
		{
			var n = new int[X[v] + 1];
			for (var k = X[v]; k >= 0; k--)
			{
				n[k] = MOD;
				if (k >= x[i]) n[k] = Min(n[k], m[k - x[i]] + y[i]);
				if (k >= y[i]) n[k] = Min(n[k], m[k - y[i]] + x[i]);
			}
			m = n;
		}
		return Y[v] = m.Min();
	}
}