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 <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
const int oo = 1e9;
const int MOD = 1000000007;
const int BASE = 26;
const int N = 200010;
#define x first
#define y second
#define pb push_back
#define mp make_pair

int n , p[1001] , x[1001], sum[1001];
vector<int> g[1001];

pii dfs(int u) {
	sum[u] = 0;
	bitset<5002> bt;
	bt[0] = 1;
	for (int i = 0; i < g[u].size(); ++i) {
		int v = g[u][i];
		pii f = dfs(v);
		sum[u] += f.x + f.y;
		bt = ((bt << f.x) | (bt << f.y));
	}
	if (!g[u].size()) {
		sum[u] = x[u];
		return mp(x[u], 0);
	}
	int add = 0 , last = -1;
	for (int k = x[u]; k >= 0 ; --k) {
		if (bt[k]) {
			last = k;
			break;
		}
	}
	if (last == -1) {
		puts("IMPOSSIBLE");
		exit(0);
	}
	add = x[u] - last;
	sum[u] += add;
	return mp(x[u], sum[u] - x[u]);
}
int main() {
	scanf("%d", &n);
	for (int i = 2; i <= n; ++i) {
		scanf("%d", &p[i]);
		g[p[i]].pb(i);
	}
	for (int i = 1 ; i <= n ; ++i)
		scanf("%d", &x[i]);
	dfs(1);
	puts("POSSIBLE");
	return 0;
}