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>

#define INF 0x3f3f3f3f

template<typename T>
inline int cmin(T &x, T y) {
	return x > y ? x = y, 1 : 0;
}

const int MAXN = 1009, MAXW = 5009;

int n, w[MAXN];
struct Edge { 
	int ver, nxt; 
} e[MAXN << 1];
int head[MAXN], tot = 0;

inline void Add(int x, int y) {
	e[++tot].ver = y, e[tot].nxt = head[x], head[x] = tot;
}

int f[MAXN], g[MAXW];

void Dfs(int x, int fa) {
	memset(g, 0x3f, sizeof g);
	g[0] = 0;
	for (int i = head[x]; i; i = e[i].nxt) {
		int y = e[i].ver;
		if (y == fa)
			continue;
		Dfs(y, x);
		for (int j = w[x]; ~j; --j) {
			int trans = INF;
			if (j >= w[y])
				cmin(trans, g[j - w[y]] + f[y]);
			if (j >= f[y])
				cmin(trans, g[j - f[y]] + w[y]);
			g[j] = trans;
		}
	}
	for (int i = 0; i <= w[x]; ++i)
		cmin(f[x], g[i]);
}

int main() {
	scanf("%d", &n);
	for (int i = 2; i <= n; ++i) {
		int f;
		scanf("%d", &f);
		Add(f, i), Add(i, f);
	}
	for (int i = 1; i <= n; ++i)
		scanf("%d", &w[i]); 

	memset(f, 0x3f, sizeof f);

	Dfs(1, 0);

	puts(f[1] == INF ? "IMPOSSIBLE" : "POSSIBLE");

	return 0;
}