Problem:
Score : 300 points

Problem Statement

You are given two integer sequences of length N: a_1,a_2,..,a_N and b_1,b_2,..,b_N.
Determine if we can repeat the following operation zero or more times so that the sequences a and b become equal.

Operation: Choose two integers i and j (possibly the same) between 1 and N (inclusive), then perform the following two actions simultaneously:

Add 2 to a_i.

Add 1 to b_j.

Constraints

1 ≤ N ≤ 10 000

0 ≤ a_i,b_i ≤ 10^9 (1 ≤ i ≤ N)

All input values are integers.

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 .. a_N
b_1 b_2 .. b_N

Output

If we can repeat the operation zero or more times so that the sequences a and b become equal, print Yes; otherwise, print No.

Sample Input 1

3
1 2 3
5 2 2

Sample Output 1

Yes

For example, we can perform three operations as follows to do our job:

First operation: i=1 and j=2. Now we have a = \{3,2,3\}, b = \{5,3,2\}.

Second operation: i=1 and j=2. Now we have a = \{5,2,3\}, b = \{5,4,2\}.

Third operation: i=2 and j=3. Now we have a = \{5,4,3\}, b = \{5,4,3\}.

Sample Input 2

5
3 1 4 1 5
2 7 1 8 2

Sample Output 2

No

Sample Input 3

5
2 7 1 8 2
3 1 4 1 5

Sample Output 3

No

Solution in Rust (1.15.1) (judge verdict: Accepted)

#![allow(unused_imports)]
#![allow(non_snake_case)]

use std::cmp::{max, min, Ordering};
use std::collections::*;
use std::io::*;
use std::ops::*;
use std::*;

// -----------------------------------------------
// Framework
// -----------------------------------------------

#[allow(unused)]
fn rl() -> String {
    let mut buf = String::new();
    io::stdin().read_line(&mut buf).unwrap();
    buf.trim_right().to_owned()
}

#[allow(unused)]
fn rw<T>() -> Vec<T>
where
    T: std::str::FromStr,
    T::Err: std::fmt::Debug,
{
    let mut buf = String::new();
    io::stdin().read_line(&mut buf).unwrap();
    buf.split_whitespace()
        .map(|word| T::from_str(word).unwrap())
        .collect()
}

trait IteratorExt: Iterator + Sized {
    fn vec(self) -> Vec<Self::Item> {
        self.collect()
    }
}

impl<T: Iterator> IteratorExt for T {}

#[allow(unused)]
macro_rules! debug {
    ($($arg:expr),*) => {
        #[cfg(debug_assertions)]
        {
            let entries = &[
                $((
                    &stringify!($arg).to_string() as &fmt::Debug,
                    &($arg) as &fmt::Debug,
                )),*
            ];
            eprintln!("{:?}", DebugMap(entries));
        }
    };
}

#[allow(unused)]
struct DebugMap<'a>(&'a [(&'a fmt::Debug, &'a fmt::Debug)]);

impl<'a> std::fmt::Debug for DebugMap<'a> {
    fn fmt(&self, fmt: &mut fmt::Formatter) -> fmt::Result {
        let mut m = fmt.debug_map();
        for &(key, value) in self.0.iter() {
            m.entry(key, value);
        }
        m.finish()
    }
}

// -----------------------------------------------
// Polyfill
// -----------------------------------------------

#[derive(PartialEq, Eq, Clone, Debug)]
pub struct Rev<T>(pub T);

impl<T: PartialOrd> PartialOrd for Rev<T> {
    fn partial_cmp(&self, other: &Rev<T>) -> Option<Ordering> {
        other.0.partial_cmp(&self.0)
    }
}

impl<T: Ord> Ord for Rev<T> {
    fn cmp(&self, other: &Rev<T>) -> Ordering {
        other.0.cmp(&self.0)
    }
}

#[allow(unused)]
macro_rules! eprintln {
    ($($arg:expr),*) => { _eprintln(format_args!($($arg),*)) }
}

fn _eprintln(args: fmt::Arguments) {
    let err = std::io::stderr();
    let mut err = err.lock();
    err.write_fmt(args).unwrap();
    err.write(b"\n").unwrap();
}

// -----------------------------------------------
// Solution
// -----------------------------------------------

fn solve(N: usize, A: &[i64], B: &[i64]) -> bool {
    let k = (0..N).map(|i| B[i] - A[i]).sum();
    if k < 0 {
        return false;
    }

    let mut ak = 0;
    let mut bk = 0;

    for i in 0..N {
        if A[i] > B[i] {
            let d = A[i] - B[i];
            bk += d;
        } else if A[i] < B[i] {
            let d = B[i] - A[i];
            ak += (d + 1) / 2;
            bk += d % 2;
        }
    }

    if ak > k || bk > k {
        return false;
    }

    return (k - bk) == (k - ak) * 2;
}

pub fn main() {
    let N: usize = rl().parse().unwrap();
    let A = rw::<i64>();
    let B = rw::<i64>();

    println!("{}", if solve(N, &A, &B) { "Yes" } else { "No" });
    return;
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test_ok() {
        assert_eq!(7, 1 + 2 * 3);
    }
}