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;
bitset<5010> can;
int fa[5010],a[5010],f[5010];
vector <int> des[5010];
int main()
{
	int n;scanf("%d",&n);
	for (int i=2;i<=n;i++) {scanf("%d",&fa[i]);des[fa[i]].push_back(i);}
	for (int i=1;i<=n;i++) scanf("%d",&a[i]);
	for (int s=n;s>=1;s--)
	{
		int all=0,ad=0;
		for (int k=0;k<des[s].size();k++)
		{
			all+=min(a[des[s][k]],f[des[s][k]]);
			ad+=max(a[des[s][k]],f[des[s][k]])-min(a[des[s][k]],f[des[s][k]]);
		}
		if (a[s]<all) {puts("IMPOSSIBLE");return 0;}
		can.reset();can[0]=1;
		for (int k=0;k<des[s].size();k++)
			can|=(can<<(max(a[des[s][k]],f[des[s][k]])-min(a[des[s][k]],f[des[s][k]])));
		for (int i=a[s]-all;i>=0;i--) if (can[i]) {f[s]=all+ad-i;break;}
		//cout<<s<<' '<<f[s]<<endl;
	}  
	puts("POSSIBLE");
}