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>
#include<ctime>
#include<random>
using namespace std;

#define MAX 1002

int n;


int val[MAX];

vector<int> v[MAX];

int dp[MAX][5002];  //white : i minumum black 

int white[MAX];  //black min
int black[MAX];  //white min

inline void dfs(int b){
	for (int i = 0; i < MAX; i++){
		dp[b][i] = 0;
	}
	if (v[b].size() == 0){
		white[b] = 0;
		black[b] = 0;
		return;
	}
	for (int k = 0; k < v[b].size(); k++){
		int go = v[b][k];
		dfs(go);
		for (int j = MAX-1; j >= 0; j--){
			if (dp[b][j] == INT_MAX)continue;
			int su = dp[b][j];
			dp[b][j] = INT_MAX;
			if (j + val[go] < MAX){
				dp[b][j + val[go]] = min(dp[b][j + val[go]], su + white[go]);
			}
			if (j + black[go] < MAX){
				dp[b][j + black[go]] = min(dp[b][j + black[go]], su + val[go]);
			}
		}
	}
	white[b] = black[b] = INT_MAX;
	for (int k = 0; k < MAX; k++){
		if (dp[b][k] != INT_MAX){
			if (dp[b][k] <= val[b]){
				black[b] = min(black[b],k);
			}
		}
		if (k <= val[b]){
			white[b] = min(white[b], dp[b][k]);
		}
	}
	if (black[b] == INT_MAX || white[b] == INT_MAX){
		puts("IMPOSSIBLE");
		exit(0);
	}
}
int main(){
	for (int i = 0; i < MAX; i++){
		for (int j = 0; j < 5002; j++){
			dp[i][j] = INT_MAX;
		}
	}
	cin >> n;
	for (int i = 1; i < n; i++){
		int p;
		scanf("%d", &p);
		p--;
		v[p].push_back(i);
	}
	for (int i = 0; i < n; i++){
		scanf("%d", &val[i]);
	}
	dfs(0);
	puts("POSSIBLE");
	return 0;
}