Problem:
Score : 500 points

Problem Statement

On a two-dimensional plane, there are m lines drawn parallel to the x axis, and n lines drawn parallel to the y axis.
Among the lines parallel to the x axis, the i-th from the bottom is represented by y = y_i.
Similarly, among the lines parallel to the y axis, the i-th from the left is represented by x = x_i.

For every rectangle that is formed by these lines, find its area, and print the total area modulo 10^9+7.

That is, for every quadruple (i,j,k,l) satisfying 1\leq i < j\leq n and 1\leq k < l\leq m, find the area of the rectangle formed by the lines x=x_i, x=x_j, y=y_k and y=y_l, and print the sum of these areas modulo 10^9+7.

Constraints

2 \leq n,m \leq 10^5

-10^9 \leq x_1 < ... < x_n \leq 10^9

-10^9 \leq y_1 < ... < y_m \leq 10^9

x_i and y_i are integers.

Input

Input is given from Standard Input in the following format:

n m
x_1 x_2 ... x_n
y_1 y_2 ... y_m

Output

Print the total area of the rectangles, modulo 10^9+7.

Sample Input 1

3 3
1 3 4
1 3 6

Sample Output 1

60

The following figure illustrates this input:

The total area of the nine rectangles A, B, ..., I shown in the following figure, is 60.

Sample Input 2

6 5
-790013317 -192321079 95834122 418379342 586260100 802780784
-253230108 193944314 363756450 712662868 735867677

Sample Output 2

835067060

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

use std::io::{self, Stdin};
use std::str::{self, FromStr};
use std::error::Error;

const MOD: i64 = 1000000007;
fn exec() {
    let mut sc = Scanner::new();
    let (n, m): (usize, usize) = (sc.ne(), sc.ne());
    let tate: Vec<i64> = (0..n).map(|_| sc.ne()).collect();
    let yoko: Vec<i64> = (0..m).map(|_| sc.ne()).collect();
    let mut tate1 = vec![0i64; n - 1];
    for i in 0..n - 1 {
        let l = i as i64 + 1;
        let r = (n - i - 1) as i64;
        tate1[i] = (l * r) % MOD;
        // println!("{} {} {}", l, r, tate1[i]);
    }
    let mut yoko1 = vec![0i64; m - 1];
    for i in 0..m - 1 {
        let l = i as i64 + 1;
        let r = (m - i - 1) as i64;
        yoko1[i] = (l * r) % MOD;
    }
    let mut tsum = 0i64;
    for i in 0..n - 1 {
        let haba = (tate[i + 1] - tate[i]) % MOD;
        tsum += haba * tate1[i];
        tsum %= MOD;
    }
    // println!("{}", tsum);
    let mut sum = 0i64;
    for i in 0..m - 1 {
        let haba = (yoko[i + 1] - yoko[i]) % MOD;
        sum += (tsum * haba) % MOD * yoko1[i];
        sum %= MOD;
    }
    println!("{}", sum);
}

fn main() {
    const STACK: usize = 16 * 1024 * 1024;
    let _ = std::thread::Builder::new()
        .stack_size(STACK)
        .spawn(|| { exec(); })
        .unwrap()
        .join()
        .unwrap();
}

#[allow(dead_code)]
struct Scanner {
    stdin: Stdin,
    id: usize,
    buf: Vec<u8>,
}

#[allow(dead_code)]
impl Scanner {
    fn new() -> Scanner {
        Scanner {
            stdin: io::stdin(),
            id: 0,
            buf: Vec::new(),
        }
    }
    fn next_line(&mut self) -> Option<String> {
        let mut res = String::new();
        match self.stdin.read_line(&mut res) {
            Ok(0) => None,
            Ok(_) => Some(res),
            Err(why) => panic!("error in read_line: {}", why.description()),
        }
    }
    fn next<T: FromStr>(&mut self) -> Option<T> {
        while self.buf.len() == 0 {
            self.buf = match self.next_line() {
                Some(r) => {
                    self.id = 0;
                    r.trim().as_bytes().to_owned()
                }
                None => return None,
            };
        }
        let l = self.id;
        assert!(self.buf[l] != b' ');
        let n = self.buf.len();
        let mut r = l;
        while r < n && self.buf[r] != b' ' {
            r += 1;
        }
        let res = match str::from_utf8(&self.buf[l..r]).ok().unwrap().parse::<T>() {
            Ok(s) => Some(s),
            Err(_) => {
                panic!("parse error, {:?}",
                       String::from_utf8(self.buf[l..r].to_owned()))
            }
        };
        while r < n && self.buf[r] == b' ' {
            r += 1;
        }
        if r == n {
            self.buf.clear();
        } else {
            self.id = r;
        }
        res
    }
    fn ne<T: FromStr>(&mut self) -> T {
        self.next::<T>().unwrap()
    }
}