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 Rust (1.42.0) (judge verdict: Accepted)

use std::fmt;
use std::io::stdin;
use std::io::BufRead;
use std::str;
use std::str::FromStr;

fn main() {
    let stdin = stdin();
    let mut scan = InputScanner::new(stdin.lock(),256);

    let n:usize = scan.next();
    let p:Vec<usize> = (0..(n-1)).map(|_| scan.next::<usize>()-1).collect();
    let x:Vec<usize> = (0..n).map(|_| scan.next()).collect();

    let mut tree:Vec<Vec<usize>> = Vec::with_capacity(n);
    tree.resize(n,Vec::new());

    for i in 0..(n-1) {
        tree[p[i]].push(i+1);
    }

    if search(0,n,&tree,&x).is_some() {
        println!("POSSIBLE");
    } else {
        println!("IMPOSSIBLE");
    }
}
fn search(i:usize,n:usize,tree:&Vec<Vec<usize>>,x:&Vec<usize>) -> Option<(usize,usize)> {
    let sub_tree = &tree[i];

    if sub_tree.is_empty() {
        Some((x[i],0))
    } else {
        let mut children = Vec::with_capacity(sub_tree.len());

        let mut sw = 0;
        let mut sb = 0;

        for &j in sub_tree {
            let child = search(j,n,tree,x)?;
            let &(w,b) = &child;
            children.push(child);
            sw += w;
            sb += b;
        }

        let sum = sw + sb;

        if x[i] == 0 {
            if sw == 0 {
                return Some((0, sb));
            } else {
                return Some((0, sw));
            }
        }

        let mut dp:Vec<bool> = (0..(x[i]+1)).map(|_| false).collect();

        dp[0] = true;

        for child in &children {
            let prev = dp;
            dp = (0..(x[i]+1)).map(|_| false).collect();

            let &(w,b) = child;

            for j in 0..(x[i]+1) {
                if w <= j {
                    dp[j] |= prev[j-w];
                }

                if b <= j {
                    dp[j] |= prev[j-b];
                }
            }

            if w > 0 && b > 0 {
                dp[0] = false;
            }
        }

        for j in (0..(x[i] + 1)).rev() {
            if dp[j] {
                return Some((x[i],sum - j))
            }
        }

        None
    }
}
struct InputScanner<R: BufRead> {
	reader: R,
	buf: Vec<u8>, // Should never be empty
	pos: usize,   // Should never be out of bounds as long as the input ends with '\n'
}
impl<R: BufRead> InputScanner<R> {
	fn new(reader: R, capacity: usize) -> Self {
		InputScanner {
			reader: reader,
			buf: Vec::with_capacity(capacity),
			pos: 0,
		}
	}

	#[inline]
	fn next<T: FromStr>(&mut self) -> T
	where
		T::Err: fmt::Debug,
	{
		if self.buf.is_empty() {
			self._read_next_line();
		}
		let mut start = None;
		loop {
			match (self.buf[self.pos], start.is_some()) {
				(b' ', true) | (b'\n', true) | (b'\r', true) => break,
				(_, true) | (b' ', false) => self.pos += 1,
				(b'\n', false) | (b'\r', false) => self._read_next_line(),
				(_, false) => start = Some(self.pos),
			}
		}
		let target = &self.buf[start.unwrap()..self.pos];
		unsafe { str::from_utf8_unchecked(target) }.parse().unwrap()
	}

	#[inline]
	fn _read_next_line(&mut self) {
		self.pos = 0;
		self.buf.clear();
		if self.reader.read_until(b'\n', &mut self.buf).unwrap() == 0 {
			panic!("Reached EOF");
		}
	}
}