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, unused_macros, unknown_lints)]

use std::collections::*;
use std::cmp::Ordering::*;

macro_rules! dump {($($e:expr), +) => {print!(concat!($(stringify!($e), " = {:?}\n"), +), $($e), +)}}
macro_rules! max {($e0:expr, $($e:expr), +) => {{let mut r = $e0; $(r = std::cmp::max(r, $e);)+ r}}}
macro_rules! min {($e0:expr, $($e:expr), +) => {{let mut r = $e0; $(r = std::cmp::min(r, $e);)+ r}}}

fn main() {
  let _ = get::val::<usize>();
  let xs = get::vec::<usize>();
  let ys = get::vec::<usize>();

  let sumx = xs.iter().sum::<usize>();
  let sumy = ys.iter().sum::<usize>();

  let d =
    xs.into_iter().zip(ys.into_iter()).
    map(|(x,y)| if x>y {0} else {y-x+1}/2).sum::<usize>();
  
  let ans = if sumx<=sumy && d <= sumy-sumx {"Yes"} else {"No"};
  println!("{}", ans)
}

struct Graph {
  size: usize,
  adj: Vec<Vec<(usize, isize)>>
}

impl Clone for Graph {
  fn clone(&self) -> Graph {
    Graph {
      size: self.size,
      adj: self.adj.clone()
    }
  }
}

#[allow(dead_code)]
impl Graph {
  fn new_nonlabeled(n: usize, edges: &[(usize, usize)]) -> Graph {
    let edges = edges.iter().map(|&(a,b)|(a,b,1)).collect::<Vec<_>>();
    Graph::new_labeled(n, &edges)
  }

  fn new_labeled(n: usize, edges: &[(usize, usize, isize)]) -> Graph {
    let mut g: Vec<Vec<(usize, isize)>> = vec![vec![]; n+1];
    for &(a, b, c) in edges {
      g[a].push((b,c));
      g[b].push((a,c));  // delete for digraph
    }
    Graph {size: n, adj: g}
  }

  fn edges(&self) -> Vec<(usize, usize, isize)> {
    let mut buf = vec![];
    for (i, next) in self.adj.iter().enumerate() {
      for &(j, x) in next {
        buf.push((i, j, x))
      }
    }
    buf
  }

  fn path(&self, v: usize, n: usize) -> Vec<Vec<usize>> {
    fn go(g: &Graph, v: usize, n: usize, mut acc: Vec<usize>, buf: &mut Vec<Vec<usize>>) {
      if n == 0 {buf.push(acc.clone()); return}
      for &(w,_) in &g.adj[v] {
        acc.push(w);
        go(g, w, n-1, acc.clone(), buf);
        let _ = acc.pop();
      }
    }

    let mut buf = vec![];
    let acc = vec![v];
    go(self, v, n, acc.clone(), &mut buf);
    buf
  }

  fn extract<F>(&self, p: F) -> Vec<usize> where F: Fn(usize) -> bool {
    (1..self.size+1).into_iter().filter(|&v|p(v)).collect()
  }

  fn degree(&self, v: usize) -> usize {
    self.adj[v].len()
  }

  fn is_adjacent(&self, u: usize, v: usize) -> bool {
    self.adj[u].iter().any(|&(w,_)|w==v) || self.adj[v].iter().any(|&(w,_)|w==u)
  }

  fn is_connected(&self) -> bool {
    self.dfs(1).len() == self.size
  }

  fn is_hitofude(&self) -> bool {
    let deg_odd = self.adj.iter().filter(|vs|vs.len()%2==1).count();
    deg_odd == 0 || deg_odd == 2
  }

  fn bellman_ford(&self, s: usize) -> Vec<isize> {
    const INF: isize = std::isize::MAX >> 1;
    let edges = self.edges();
    let mut bf: Vec<isize> = vec![INF; self.size];
    bf[s] = 0;

    for _ in 1 .. self.size {
      for &(v, w, c) in &edges {
        bf[w] = std::cmp::min(bf[w], bf[v]+c)
      }
    }
    bf
  }

  fn dijkstra(&self, s: usize) -> Vec<isize> {
    use std::collections::BinaryHeap;

    const INF: isize = std::isize::MAX;
    let mut dk: Vec<isize> = vec![INF; self.size+1];
    dk[s] = 0;

    let mut pq = BinaryHeap::new();
    pq.push((0,s));

    while let Some((acc,v)) = pq.pop() {
      let acc = -acc;
      for &(w,c) in &self.adj[v] {
        let cand = acc + c;
        if cand < dk[w] {
          if dk[w] != INF {println!("No"); std::process::exit(0)}
          dk[w] = cand;
          pq.push((-cand,w));
        }
      }
    }
    dk
  }

  fn warshall_floyd(&self) -> Vec<Vec<isize>> {
    const INF: isize = std::isize::MAX >> 1;
    let mut wf: Vec<Vec<isize>> = vec![vec![INF; self.size+1]; self.size+1];
    for i in 1 .. self.size+1 {wf[i][i] = 0}

    for (next, i) in self.adj.iter().zip(0..) {
      for &(j, x) in next {
        wf[i][j] = x
      }
    }
    for k in 1 .. self.size+1 {
      for i in 1 .. self.size+1 {
        for j in 1 .. self.size+1 {
          wf[i][j] = std::cmp::min(wf[i][j], wf[i][k] + wf[k][j]);
        }
      }
    }
    wf
  }

  fn coloring2(&self) -> Option<(Vec<usize>, Vec<usize>)> {
    fn paint(v: usize, p: bool, g: &Graph, cv: &mut Vec<Option<bool>>) -> bool {
      match cv[v] {
        None => {
          let next = &g.adj[v];
          cv[v] = Some(p);
          next.iter().all(|&(w,_)|paint(w,!p,g,cv))},
        Some(q) => {q == p}
      }
    }

    let mut canvas: Vec<Option<bool>> = vec![None; self.size+1];
    let ans = paint(1, false, self, &mut canvas);
    let bs = canvas.iter().enumerate().filter(|&(_,&v)|v==Some(false)).map(|(i,_)|i).collect::<Vec<_>>();
    let ws = canvas.iter().enumerate().filter(|&(_,&v)|v==Some(true)).map(|(i,_)|i).collect::<Vec<_>>();
    if ans {Some((bs,ws))} else {None}
  }

  fn dfs(&self, s: usize) -> Vec<usize> {
    fn go(g: &Graph, current: usize, mut path: &mut Vec<usize>, mut visited: &mut Vec<bool>) {
      for &(next, _) in &g.adj[current] {
        if visited[next] {
          continue
        } else {
          visited[next] = true;
          path.push(next);
          go(&g, next, &mut path, &mut visited)
        }
      }
    }

    let mut path = vec![s];
    let mut visited = vec![false; self.size+1];
    visited[s] = true;
    go(&self, s, &mut path, &mut visited);
    path
  }

  fn bfs(&self, v: usize) -> Vec<usize> {
    use std::collections::VecDeque;
    let mut q = VecDeque::new();
    let mut buf = vec![];
    let mut vd = vec![false; self.size+1];
    vd[v] = true;
    q.push_back(v);
    while let Some(w) = q.pop_front() {
      buf.push(w);
      for &(next,_) in self.adj[w].iter() {
        if !vd[next] {
          q.push_back(next);
          vd[next] = true
        }
      }
    }
    buf
  }

  fn ultimate(&self, v: usize) -> usize {
    use std::collections::VecDeque;
    let mut q = VecDeque::new();
    let mut dist = 0;
    let mut vd = vec![false; self.size+1];
    vd[v] = true;
    q.push_back((v,dist));
    while let Some((w, d)) = q.pop_front() {
      dist = std::cmp::max(dist, d);
      for &(next,_) in self.adj[w].iter() {
        if !vd[next] {
          q.push_back((next, d+1));
          vd[next] = true
        }
      }
    }
    dist
  }

  fn cut(&mut self, v: usize, w: usize) {
    self.adj[v].retain(|&(t,_)| t != w);
    self.adj[w].retain(|&(t,_)| t != v);
  }
}

#[allow(dead_code)]
mod get {
  use std::io::*;
  use std::str::*;
  use std::process::*;

  pub fn val<T: FromStr>() -> T {
    let mut buf = String::new();
    let s = stdin();
    s.lock().read_line(&mut buf).ok();
    if buf.is_empty() {println!("No input"); exit(0)}
    buf.trim_right().parse::<T>().ok().unwrap()
  }

  pub fn vals<T: FromStr>(n: usize) -> Vec<T> {
    let mut vec: Vec<T> = vec![];
    for _ in 0 .. n {
      vec.push(val());
    }
    vec
  }

  pub fn tuple<T1: FromStr, T2: FromStr>() -> (T1, T2) {
    let mut buf = String::new();
    let s = stdin();
    s.lock().read_line(&mut buf).ok();
    if buf.is_empty() {println!("No input"); exit(0)}
    let mut it = buf.trim_right().split_whitespace();
    let x = it.next().unwrap().parse::<T1>().ok().unwrap();
    let y = it.next().unwrap().parse::<T2>().ok().unwrap();
    (x, y)
  }

  pub fn tuples<T1: FromStr, T2: FromStr>(n: usize) -> Vec<(T1, T2)> {
    let mut vec: Vec<(T1, T2)> = vec![];
    for _ in 0 .. n {
      vec.push(tuple());
    }
    vec
  }

  pub fn tuple3<T1: FromStr, T2: FromStr, T3: FromStr>() -> (T1, T2, T3) {
    let mut buf = String::new();
    let s = stdin();
    s.lock().read_line(&mut buf).ok();
    if buf.is_empty() {println!("No input"); exit(0)}
    let mut it = buf.trim_right().split_whitespace();
    let x = it.next().unwrap().parse::<T1>().ok().unwrap();
    let y = it.next().unwrap().parse::<T2>().ok().unwrap();
    let z = it.next().unwrap().parse::<T3>().ok().unwrap();
    (x, y, z)
  }

  pub fn tuple3s<T1: FromStr, T2: FromStr, T3: FromStr>(n: usize) -> Vec<(T1, T2, T3)> {
    let mut vec: Vec<(T1, T2, T3)> = vec![];
    for _ in 0 .. n {
      vec.push(tuple3());
    }
    vec
  }

  pub fn vec<T: FromStr>() -> Vec<T> {
    let mut buf = String::new();
    let s = stdin();
    s.lock().read_line(&mut buf).ok();
    if buf.is_empty() {println!("No input"); exit(0)}
    buf.trim_right().split_whitespace().map(|t| t.parse::<T>().ok().unwrap()).collect()
  }

  pub fn mat<T: FromStr>(h: usize) -> Vec<Vec<T>> {
    let mut mat = vec![];
    for _ in 0 .. h {
      mat.push(vec());
    }
    mat
  }

  pub fn chars() -> Vec<char> {
    let mut buf = String::new();
    let s = stdin();
    s.lock().read_line(&mut buf).ok();
    if buf.is_empty() {println!("No input"); exit(0)}
    buf.trim_right().chars().collect()
  }
}

#[allow(dead_code)]
mod put {
  use std::string::*;

  pub fn vec<T: ToString>(vec: &Vec<T>, sep: &str) {
    let out = vec.iter().map(|e| e.to_string()).collect::<Vec<_>>().as_slice().join(sep);
    println!("{}", out);
  }

  pub fn mat<T: ToString>(mat: &Vec<Vec<T>>, sep: &str) {
    for v in mat {
      vec(v, sep);
    }
  }
}