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)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using static System.Console;
using static System.Math;

namespace AtTest._700problems
{
    class ARC083_E
    {
        static void Main(string[] args)
        {
            Method(args);
        }

        static void Method(string[] args)
        {
            int n = ReadInt();
            if (n == 1)
            {
                Read();
                Read();
                WriteLine("POSSIBLE");
                return;
            }

            int[] ps = ReadInts();
            int[] xs = ReadInts();

            int[] childCnt = new int[n];
            for(int i = 0; i < ps.Length; i++)
            {
                childCnt[ps[i] - 1]++;
            }
            
            var pairList = new List<KeyValuePair<int, int>>[n];
            for (int i = 0; i < n; i++)
            {
                pairList[i] = new List<KeyValuePair<int, int>>();
            }

            var queue = new Queue<int>();
            for(int i = 0; i < n; i++)
            {
                if (childCnt[i] == 0)
                {
                    queue.Enqueue(i);
                    pairList[i].Add(new KeyValuePair<int, int>(0, 0));
                }
            }

            while (queue.Count > 0)
            {
                int index = queue.Dequeue();
                var dp = new HashSet<int>();
                dp.Add(0);
                int sum = 0;
                for(int i = 0; i < pairList[index].Count; i++)
                {
                    var pair = pairList[index][i];

                    var next = new HashSet<int>();
                    foreach(int val2 in dp)
                    {
                        int val1 = sum - val2;
                        if (val1 + pair.Key <= xs[index])
                        {
                            next.Add(val2 + pair.Value);
                        }
                        if (val1 + pair.Value <= xs[index])
                        {
                            next.Add(val2 + pair.Key);
                        }
                    }

                    dp = next;
                    sum += pair.Key + pair.Value;
                }

                int min = int.MaxValue;
                foreach(int val in dp)
                {
                    min = Min(min, val);
                }

                if (min == int.MaxValue)
                {
                    WriteLine("IMPOSSIBLE");
                    return;
                }

                if (index == 0) continue;

                int parent = ps[index - 1] - 1;
                pairList[parent].Add(
                    new KeyValuePair<int, int>(xs[index], min));
                childCnt[parent]--;
                if (childCnt[parent] == 0)
                {
                    queue.Enqueue(parent);
                }
            }

            WriteLine("POSSIBLE");
        }

        private static string Read() { return ReadLine(); }
        private static char[] ReadChars() { return Array.ConvertAll(Read().Split(), a => a[0]); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }
    }
}