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: Runtime Error)

using System;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Collections;
using System.Collections.Generic;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using static System.Math;
using LayoutKind = System.Runtime.InteropServices.LayoutKind;
using StructLayoutAttribute = System.Runtime.InteropServices.StructLayoutAttribute;
using FieldOffsetAttribute = System.Runtime.InteropServices.FieldOffsetAttribute;
using MethodImplOptions = System.Runtime.CompilerServices.MethodImplOptions;
using MethodImplAttribute = System.Runtime.CompilerServices.MethodImplAttribute;

static class P
{
    static void Main()
    {
        int n = int.Parse(Console.ReadLine());
        var p = Console.ReadLine().Split().Select(x => int.Parse(x) - 1).ToArray();
        var X = Console.ReadLine().Split().Select(int.Parse).ToArray();
        var childlen = Enumerable.Repeat(0, n).Select(_ => new List<int>()).ToArray();
        for (int i = 0; i < p.Length; i++) childlen[p[i]].Add(i + 1);
        Stack<int> stack = new Stack<int>();
        stack.Push(0);
        List<int> order = new List<int>();
        while (stack.Count > 0)
        {
            int elem = stack.Pop();
            order.Add(elem);
            foreach (var child in childlen[elem]) stack.Push(child);
        }
        Tuple<int, int>[] bw = new Tuple<int, int>[n];
        foreach (var elem in order.Reverse<int>())
        {
            //Xまで詰めたい
            List<bool> knapsack = new bool[X[elem] + 1].ToList();
            knapsack[0] = true;
            int totalSum = 0;
            foreach (var child in childlen[elem])
            {
                totalSum += bw[child].Item1;
                totalSum += bw[child].Item2;
                for (int i = knapsack.Count - 1; i >= 0; i--)
                {
                    if (!knapsack[i]) continue;
                    knapsack[i] = false;
                    if (i + bw[child].Item1 < knapsack.Count) knapsack[i + bw[child].Item1] = true;
                    if (i + bw[child].Item2 < knapsack.Count) knapsack[i + bw[child].Item2] = true;
                }
            }
            var count = knapsack.LastIndexOf(true);
            if(count == -1)
            {
                Console.WriteLine("IMPOSSIBLE");
                return;
            }
            bw[elem] = new Tuple<int, int>(totalSum - count, X[elem]);
        }
        Console.WriteLine("POSSIBLE");
    }
}