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 (1.42.0) (judge verdict: Accepted)

use std::io::*;
const MOD: i64 = 1_000_000_007;

fn main() {
    let mut s: String = String::new();
    std::io::stdin().read_to_string(&mut s).ok();
    let mut itr = s.trim().split_whitespace();
    let n: usize = itr.next().unwrap().parse().unwrap();
    let m: usize = itr.next().unwrap().parse().unwrap();
    let x: Vec<i64> = (0..n)
        .map(|_| itr.next().unwrap().parse().unwrap())
        .collect();
    let y: Vec<i64> = (0..m)
        .map(|_| itr.next().unwrap().parse().unwrap())
        .collect();
    let mut sx = x.iter().sum::<i64>();
    let mut sy = y.iter().sum::<i64>();
    let mut allx = 0i64;
    let mut ally = 0i64;
    for i in 0..n {
        sx -= x[i];
        allx += sx - x[i] * (n - 1 - i) as i64;
        allx %= MOD;
    }
    for i in 0..m {
        sy -= y[i];
        ally += sy - y[i] * (m - 1 - i) as i64;
        ally %= MOD;
    }
    println!("{}", allx * ally % MOD);
}