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 (GCC 9.2.1) (judge verdict: Accepted)

#include <stdio.h>

typedef struct List {
	struct List *next;
	int v;
} list;

int main()
{
	int i, N, P[1001], X[1001];
	scanf("%d", &N);
	for (i = 2, P[1] = 1; i <= N; i++) scanf("%d", &(P[i]));
	for (i = 1; i <= N; i++) scanf("%d", &(X[i]));
	
	list *adj[1001] = {}, e[1003];
	for (i = 2; i <= N; i++) {
		e[i].v = i;
		e[i].next = adj[P[i]];
		adj[P[i]] = &(e[i]);
	}
	
	int q[1001], head, tail;
	list *p;
	q[0] = 1;
	for (head = 0, tail = 1; head < tail; head++) {
		for (p = adj[q[head]]; p != NULL; p = p->next) q[tail++] = p->v;
	}
	
	int u, w, min[1001] = {}, sum;
	char dp[5001];
	for (head--; head >= 0; head--) {
		u = q[head];
		for (i = 1, dp[0] = 1; i <= 5000; i++) dp[i] = 0;
		for (p = adj[u], sum = 0; p != NULL; p = p->next) {
			w = p->v;
			sum += X[w] + min[w];
			for (i = X[u]; i >= 0; i--) {
				if (dp[i] == 1) {
					dp[i] = 0;
					if (i + X[w] <= X[u]) dp[i+X[w]] = 1;
					if (i + min[w] <= X[u]) dp[i+min[w]] = 1;
				}
			}
		}
		for (i = X[u]; i >= 0; i--) if (dp[i] == 1) break;
		if (i < 0) break;
		
		min[u] = sum - i;
	}
	
	if (head >= 0) printf("IMPOSSIBLE\n");
	else printf("POSSIBLE\n");
	fflush(stdout);
	return 0;
}