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)

fn get_line() -> String {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().to_string()
}

const M: i64 = 1000000000 + 7;

fn main() {
    let nm: Vec<_> = get_line().split(' ').map(|x| x.parse().unwrap()).collect();

    let xs: Vec<i64> = get_line().split(' ').map(|x| x.parse().unwrap()).collect();
    let ys: Vec<i64> = get_line().split(' ').map(|x| x.parse().unwrap()).collect();

    let mut rx = 0;
    let mut ry = 0;
    for i in 0..nm[0] {
        rx += xs[i] * (i as i64 * 2 - nm[0] as i64 + 1);
        rx %= M;
    }
    for i in 0..nm[1] {
        ry += ys[i] * (i as i64 * 2 - nm[1] as i64 + 1);
        ry %= M;
    }

    println!("{}", rx * ry % M);
}