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 5.4.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>

using namespace std;


struct jie{
    int l,h;
    int lh;
}a[1005];
vector<int> q[1005];
const int inf=10000009;
int f=0;
int dp[5000005],b[1005];
int dfs(int u)
{
    int i,j,k,ma=0,t;
    if(q[u].size())
    {
        int sum=0,s=0,m;
        for(i=0;i<q[u].size();i++)
        {
            sum+=dfs(q[u][i]);
            s+=a[q[u][i]].h+a[q[u][i]].h;
        }
        if(sum>b[u])
        {
            f=1;
            return inf;
        }
        m=b[u]-sum;
        for(i=0;i<=m;i++)
        {
            dp[i]=0;
        }
        for(i=0;i<q[u].size();i++)
        {
            k=q[u][i];
            for(j=m;j>=a[k].lh;j--)
            {
                dp[j]=max(dp[j],dp[j-a[k].lh]+a[k].lh);
            }
        }
        for(i=0;i<=m;i++)
        {
            ma=max(ma,dp[i]);
        }
        t=sum+ma;
        s-=t;
        a[u].h=max(s,b[u]);
        a[u].l=min(s,b[u]);
        a[u].lh=a[u].h-a[u].l;
    }
    return a[u].l;
}
int main()
{
    int n,x,i;
    scanf("%d",&n);
    for(i=2;i<=n;i++)
    {
        scanf("%d",&x);
        q[x].push_back(i);
    }
    for(i=1;i<=n;i++)
    {
        scanf("%d",&b[i]);
    }
    for(i=1;i<=n;i++)
    {
        if(q[i].size()==0)
        {
            a[i].h=a[i].lh=b[i];
            a[i].l=0;
        }
    }
    dfs(1);
    if(f==1)
    {
        printf("IMPOSSIBLE\n");
    }
    else
    {
        printf("POSSIBLE\n");
    }
    return 0;

}