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(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

const MOD: u64 = 1000_000_000 + 7;

fn main() {
    let v: Vec<usize> = read_vec();
    let x = read_vec::<i64>();
    let y = read_vec::<i64>();

    let (n, m) = (v[0] - 1, v[1] - 1);
    let mut n_coef = vec![0u64; n];
    let mut m_coef = vec![0u64; m];

    for i in 0..n {
        n_coef[i] = 1 + i as u64 + (n - i - 1) as u64;
        n_coef[i] %= MOD;
        n_coef[i] += (i * (n - i - 1)) as u64;
        n_coef[i] %= MOD;
    }

    for i in 0..m {
        m_coef[i] = 1 + i as u64 + (m - i - 1) as u64;
        m_coef[i] %= MOD;
        m_coef[i] += (i * (m - i - 1)) as u64;
        m_coef[i] %= MOD;
    }

    let x = (1..n + 1)
        .map(|i| (x[i] - x[i - 1]) as u64)
        .collect::<Vec<_>>();
    let y = (1..m + 1)
        .map(|i| (y[i] - y[i - 1]) as u64)
        .collect::<Vec<_>>();

    let x_areas = (0..n).fold(0, |s, i| (s + (x[i] * n_coef[i]) % MOD) % MOD);
    let y_areas = (0..m).fold(0, |s, i| (s + (y[i] * m_coef[i]) % MOD) % MOD);
    let ans = (x_areas * y_areas) % MOD;
    println!("{:?}", ans);
}