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;

#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;

typedef unsigned long long ull;
typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;

// order statistics tree
typedef tree<pii, null_type, less<pii>, rb_tree_tag,
             tree_order_statistics_node_update> indexed_set;

#define F first
#define S second
#define PB push_back
#define MP make_pair

#define rep(i, a, b) for(int i = a; i < (b); ++i)
#define rrep(i, b, a) for(int i = b; i >= a; --i)
#define trav(a, x) for(auto& a : x)
#define all(x) x.begin(), x.end()
#define sz(x) (int)(x).size()

const int N = 1001;
const int INF = 1e9;
const int X = 5001;
int n;
int parent[N];
vector<int> children[N];
int weight[N];
int other_weight[N];
bool visited[N];

bool possible;

void lrn(int v){
  if(!possible) return;

  trav(c, children[v]){
    lrn(c);
  }

  int nc = sz(children[v]);

  int hi = weight[v];

  // [# children used][weight of white] = is possible?
  bool dp[nc][hi+1];

  memset(dp, false, sizeof(dp));

  dp[0][0] = true;

  int total = 0;
  rep(i, 1, nc){
    int c = children[v][i];
    int wc = weight[c], owc = other_weight[c];

    total += wc + owc;

    rep(w, 0, hi+1){
      if(!dp[i-1][w]) continue;

      if(w + wc <= hi) dp[i][w+wc] = true;
      if(w + owc <= hi) dp[i][w+owc] = true;
    }
  }

  int ans = -1;
  rrep(w, hi, 0){
    if(dp[nc-1][w]){
      ans = total - w;
      break;
      // printf("ans: %d\n", ans);
    }
  }

  if(ans == -1){
    possible = false;
  } else {
    other_weight[v] = ans;
  }
}

int main() {
  cin.tie(0); cin.exceptions(cin.failbit);

  bool possible = true;

  scanf("%d", &n);

  // all a null child to the beginning of each vector
  rep(i, 1, n+1){
    children[i].PB(0);
  }

  rep(i, 2, n+1){
    scanf("%d", parent+i);
    children[parent[i]].PB(i);
  }
  rep(i, 1, n+1) scanf("%d", weight+i);

  possible = true;

  lrn(1);

  printf("%s\n", possible ? "POSSIBLE" : "IMPOSSIBLE");
  return 0;
}