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 NMAX = 1000 + 5;

int N;
int X[NMAX];
vector <int> graph[NMAX];

pair <int, int> p[NMAX];

int dp[5005];
void updMin(int &where, int val) {
    if (val < where)
        where = val;
}

void dfs(int node) {
    for (auto it: graph[node])
        dfs(it);

    for (int i = 0; i <= 5001; ++ i)
        dp[i] = 1E9 + 256;
    dp[0] = 0;
    for (auto it: graph[node]) {
        int a = p[it].first, b = p[it].second;
        for (int val = 5001; val >= 0; -- val) {
            int x = dp[val];
            dp[val] = 1E9 + 256;
            updMin(dp[min(5001, val + a)], min(5001, x + b));
            updMin(dp[min(5001, val + b)], min(5001, x + a));
        }
    }

    p[node].first = X[node];
    p[node].second = 1E9 + 256;
    for (int i = 0; i <= X[node]; ++ i)
        p[node].second = min(p[node].second, dp[i]);

    if (p[node].second >= 1E9 / 2) {
        cout << "IMPOSSIBLE\n";
        exit(0);
    }
}

int main()
{
    ios_base :: sync_with_stdio(false);
    //freopen("data.in", "r", stdin);

    cin >> N;
    for (int i = 2; i <= N; ++ i) {
        int p;
        cin >> p;
        graph[p].push_back(i);
    }
    for (int i = 1; i <= N; ++ i)
        cin >> X[i];
    dfs(1);

    cout << "POSSIBLE\n";
    return 0;
}