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)

#![allow(dead_code)]
macro_rules! debug {
    ($($arg:tt)*) => (if cfg!(debug_assertions) {print!("[DEBUG] "); println!($($arg)*)});
}

fn f(b: i64, n: i64) -> i64 {
    return if n < b {
        n
    } else {
        f(b, n / b) + n % b
    };
}

const MOD: i64 = (1e9 + 7.) as i64;

fn calc(a: Vec<i64>) -> i64 {
    let n = a.len() - 1;
    let mut x = vec![0i64; n];
    for i in 0..n {
        x[i] = a[i + 1] - a[i];
        debug!("x[{}]={}", i, x[i]);
    }

    let mut xs = vec![0i64; n + 1];
    let mut xss = vec![0i64; n + 1];
    let mut xsum: i64 = 0;
    for i in 0..n {
        xs[i + 1] = xs[i] + x[i];
        xss[i + 1] = (xss[i] + xs[i + 1]) % MOD;
        debug!("xs[{}]={}, xss[{}]={}", i + 1, xs[i + 1], i + 1, xss[i + 1]);
    }
    for i in 0..n {
        xsum += (xss[n] - xss[i] + MOD) - xs[i] * (n - i) as i64 % MOD;
        xsum = (xsum + MOD) % MOD;
        debug!("i={}, xsum={}", i, xsum);
    }
    xsum
}

fn main() {
    let mut rd = reader::Reader::new();

    let n: usize = rd.next();
    let m: usize = rd.next();

    let x: Vec<i64> = rd.next_n(n);
    let y: Vec<i64> = rd.next_n(m);

    println!("{}", calc(x) * calc(y) % MOD);
}

mod reader {
    use std::fmt::Debug;
    use std::str::FromStr;
    use std::collections::VecDeque;
    use std::io::{self, Read};

    fn _read_line() -> String {
        let mut buf = String::new();
        let _ = io::stdin().read_to_string(&mut buf);
        buf
    }

    fn _read_vec_deque_string() -> VecDeque<String> {
        _read_line()
            .split_whitespace()
            .map(|s| s.to_string())
            .collect()
    }

    pub struct Reader {
        buf: VecDeque<String>,
    }

    impl Reader {
        pub fn new() -> Reader {
            Reader { buf: VecDeque::new() }
        }

        fn update_buf(&mut self) {
            if self.buf.is_empty() {
                self.buf = _read_vec_deque_string();
            }
        }

        pub fn next<T>(&mut self) -> T
            where
                T: FromStr,
                T::Err: Debug,
        {
            self.update_buf();
            self.buf.pop_front().unwrap().parse::<T>().unwrap()
        }

        pub fn next_n<T>(&mut self, n: usize) -> Vec<T>
            where
                T: FromStr,
                T::Err: Debug,
        {
            let mut vec: Vec<T> = Vec::with_capacity(n);

            for _ in 0..n {
                vec.push(self.next());
            }
            vec
        }
    }
}