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 <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>

const int MAXN = 1e3;

int n, edge;
int X[MAXN | 1], fst[MAXN | 1];
int sum[MAXN | 1], dp[MAXN | 1][5001];

struct Edge {
  int to, nxt;
  Edge() : to(0), nxt(0) {}
  Edge(int a, int b) : to(b), nxt(fst[a]) {}
} e[MAXN];

inline int read() {
  register int x = 0;
  register char ch = getchar();
  while (!isdigit(ch)) ch = getchar();
  while (isdigit(ch)) {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return x;
}

inline void addEdge(int a, int b) {
  e[++edge] =  Edge(a, b);
  fst[a] = edge;
}

void DP(int x) {
  int size = 0;
  for (int k = fst[x], i = 1; k; k = e[k].nxt, ++i) {
    int to = e[k].to;
    DP(to);
    sum[x] += sum[to];
    ++size;
  }
  memset(dp, 0, sizeof(dp));
  dp[0][0] = 1;
  for (int k = fst[x], i = 1; k; k = e[k].nxt, ++i) {
    int to = e[k].to;
    for (int j = 0; j <= X[x]; ++j) {
      if (j >= X[to]) dp[i][j] = dp[i - 1][j - X[to]] + dp[i - 1][j - X[to]];
      if (j - sum[to] + X[to] >= 0) dp[i][j] = dp[i - 1][j - sum[to] + X[to]] + dp[i - 1][j - sum[to] + X[to]];
    }
  }
  bool flag = false;
  for (int i = X[x] - 1; i >= 0; --i) {
    if (dp[size][i] || dp[size][i]) {
      flag = true;
      sum[x] += X[x] - i; 
      // printf("x=%d i=%d\n", x, i);
      break;
    }
  }
  if (!flag) {
    puts("IMPOSSIBLE");
    exit(0);
  }
}

int main() {;
  n = read();
  for (int i = 2; i <= n; ++i) addEdge(read(), i);
  for (int i = 1; i <= n; ++i) X[i] = read();
  DP(1);
  puts("POSSIBLE");
  // for (int i = 1; i <= n; ++i) printf("%d ", sum[i]);
  return 0;
}