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: Accepted)

#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
using ll = long long int;

const int MAX_X = 5050;
const int MAX_N = 1010;

vector<vector<int>> edge(MAX_N);
vector<int> xs;

pair<int, int> dfs(int n){
    int total = xs[n];
    if((int)edge[n].size() == 0){
        return pair<int, int>{0, total};
    }
    vector<int> dp(MAX_X, 0);
    int child_sum = 0;
    for(int i=0; i<(int)edge[n].size(); i++){
        pair<int, int> ret = dfs(edge[n][i]);
        if(ret.first == -1){
            return pair<int, int>{-1, -1};
        }
        child_sum += ret.first + ret.second;
        if(i == 0){
            if(ret.first <= total){
                dp[ret.first] = 1;
            }
            if(ret.second <= total){
                dp[ret.second] = 1;
            }
            continue;
        }
        // Search possible values 
        for(int j=total; j>-1; j--){
            if(dp[j] == 1){
                dp[j] = 0;
                if(j + ret.second <= total){dp[j + ret.second] = 1;}
                if(j + ret.first <= total){dp[j + ret.first] = 1;}
            }
        }
    }
    for(int i=total; i>-1; i--){
        if(dp[i] == 1){
            int a = total;
            int b = child_sum - i;
            if(a > b){swap(a, b);}
            return pair<int, int>{a, b};
        }
    }
    return pair<int, int>{-1, -1};
}

int main() {
    int n; cin >> n;
    for(int i=0; i<n-1; i++){
        int p; cin >> p; p--;
        edge[p].push_back(i+1);
    }
    for(int i=0; i<n; i++){
        int x; cin >> x;
        xs.push_back(x);
    }
    pair<int, int> ret = dfs(0);
    // cout << ret.first << " " << ret.second << endl;
    if(ret.first == -1){
        cout << "IMPOSSIBLE" << endl;
    }
    else{
        cout << "POSSIBLE" << endl;
    }
    return 0;
}