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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>

using namespace std;

const int INF = 1 << 29;

int N, X[1001];
vector< int > g[1000];
unordered_map< int, int > dp[1000];

int main()
{

  cin >> N;
  for(int i = 1; i < N; i++) {
    int x;
    cin >> x;
    g[--x].emplace_back(i);
  }
  for(int i = 0; i < N; i++) {
    cin >> X[i];
  }

  for(int i = N - 1; i >= 0; i--) {
    if(g[i].empty()) {
      dp[i][X[i]] = 0;
      dp[i][0] = X[i];
    } else {
      unordered_map< int, int > dp2;
      dp2[0] = 0;
      for(auto &to : g[i]) {
        unordered_map< int, int > dp3;
        for(auto &s : dp2) {
          for(auto &t : dp[to]) {
            if(!dp3.count(s.first + t.first)) dp3[s.first + t.first] = s.second + t.second;
            else dp3[s.first + t.first] = min(dp3[s.first + t.first], s.second + t.second);
          }
        }
        dp3.swap(dp2);
      }

      int ret = INF;
      for(int j = X[i]; j >= 0; j--) {
        if(dp2.count(j)) ret = min(ret, dp2[j]);
      }
      if(ret != INF) dp[i][X[i]] = ret;
      for(int j = 5000; j >= 0; j--) {
        if(!dp2.count(j)) continue;
        if(dp2[j] > X[i]) continue;
        dp[i][j] = min(dp[i][j], X[i]);
      }
    }
  }

  if(dp[0].count(X[0])) {
    cout << "POSSIBLE" << endl;
  } else {
    cout << "IMPOSSIBLE" << endl;
  }
}