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 Kotlin (1.0.0) (judge verdict: Accepted)

const val INF = Int.MAX_VALUE / 4

fun main(args: Array<String>) {
  val n = readLine()!!.toInt()
  if (n == 1) {
    println("POSSIBLE")
    return
  }

  val graph = Array(n, { mutableListOf<Int>() })
  val rawParents = readLine()!!.split(" ").map(String::toInt)
  rawParents.forEachIndexed { rawIndex, rawValue ->
    val index = rawIndex + 1
    val parent = rawValue - 1
    graph[parent].add(index)
  }
  val xs = readLine()!!.split(" ").map(String::toInt)

  val dp = IntArray(n, { INF })
  fun isValid(v: Int): Boolean {
    if (graph[v].size == 0) {
      dp[v] = 0
      return true
    }
    if (graph[v].any { !isValid(it) }) {
      return false
    }

    val innerDP = Array(graph[v].size + 1, { IntArray(xs[v] + 1, { INF }) })
    innerDP[0][0] = 0
    for (i in graph[v].indices) {
      val c = graph[v][i]
      val v1 = xs[c]
      val v2 = dp[c]
      for (k1 in 0..xs[v]) {
        if (innerDP[i][k1] < INF) {
          if (k1 + v1 <= xs[v]) {
            innerDP[i + 1][k1 + v1] = Math.min(innerDP[i + 1][k1 + v1], innerDP[i][k1] + v2)
          }
          if (k1 + v2 <= xs[v]) {
            innerDP[i + 1][k1 + v2] = Math.min(innerDP[i + 1][k1 + v2], innerDP[i][k1] + v1)
          }
        }
      }
    }
    val min = innerDP[graph[v].size].min()!!
    if (min == INF) return false
    dp[v] = min
    return true
  }

  val ans = isValid(0)
  println(if (ans) "POSSIBLE" else "IMPOSSIBLE")
}