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;
use std::io::{Read, BufReader};
use std::cmp;

fn next_token<R: Read>(reader: &mut R) -> Vec<u8> {
    let mut buf: [u8; 1] = [0];
    let mut read_chars = false;
    let mut ret: Vec<u8> = vec![];

    loop {
        if reader.read(&mut buf).unwrap() == 0 {
            break;
        } else {
            if buf[0] == '\r' as u8 || buf[0] == '\n' as u8 || buf[0] == ' ' as u8 {
                if read_chars {
                    break;
                }
            } else {
                read_chars = true;
                ret.push(buf[0]);
            }
        }
    };
    ret
}
fn next_i64<R: Read>(reader: &mut R) -> i64 {
    let token = next_token(reader);
    let mut ret: i64 = 0;
    let mut sgn = false;

    for c in token {
        if '0' as u8 <= c && c <= '9' as u8 {
            ret = ret * 10 + (c - ('0' as u8)) as i64;
        } else if '-' as u8 == c {
            sgn = true;
        }
    };
    ret * if sgn { -1 } else { 1 }
}
fn next_i32<R: Read>(reader: &mut R) -> i32 {
    next_i64(reader) as i32
}
static MOD: i64 = 1000000007;

fn solve_1d(x: & Vec<i64>) -> i64 {
    let mut ret = 0;
    for i in 1..x.len() {
        let d = x[i] - x[i - 1];
        ret = (ret + (d as i64) * (i as i64) % MOD * (x.len() - i) as i64) % MOD;
    }
    ret
}
fn main() {
    let buf = &mut BufReader::new(io::stdin());

    let n = next_i32(buf);
    let m = next_i32(buf);
    let mut x: Vec<i64> = vec![];
    let mut y: Vec<i64> = vec![];
    for _ in 0..n {
        x.push(next_i64(buf));
    }
    for _ in 0..m {
        y.push(next_i64(buf));
    }
    let ret = solve_1d(&x) * solve_1d(&y) % MOD;
    println!("{}", ret);
}