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: Time Limit Exceeded)

#!/usr/bin/env run-cargo-script

use std::fmt::Debug;
use std::io;
use std::io::{Read, Stdin};
use std::str;
use std::str::FromStr;

fn main() {
    let mut sc = Scanner::new();
    let (n, m) = (sc.parse::<usize>(), sc.parse::<usize>());
    let (xs, ys) = (sc.vec::<i32>(n), sc.vec::<i32>(m));
    println!("{}", solve(xs, ys));
}


fn solve(xs: Vec<i32>, ys: Vec<i32>) -> String {
    let mut result = 0;
    for jx in 1..xs.len() {
        for ix in 0..jx {
            for jy in 1..ys.len() {
                for iy in 0..jy {
                    let w = (xs[jx] - xs[ix]) as usize;
                    let h = (ys[jy] - ys[iy]) as usize;
                    result = (result + w * h) % 1000000007;
                }
            }
        }
    }
    format!("{}", result)
}


struct Scanner {
    stdin: Stdin,
    buf: Vec<u8>,
}

impl Scanner {
    fn new() -> Scanner {
        Scanner {
            stdin: io::stdin(),
            buf: Vec::with_capacity(256),
        }
    }

    fn parse<T: FromStr>(&mut self) -> T
        where <T as FromStr>::Err: Debug
    {
        self.buf.clear();
        let mut it = self.stdin.lock().bytes();
        let mut c = it.next().unwrap().unwrap();
        while c == ' ' as u8 || c == '\n' as u8 {
            c = it.next().unwrap().unwrap();
        }
        while !(c == ' ' as u8 || c == '\n' as u8) {
            self.buf.push(c);
            c = it.next().unwrap().unwrap();
        }
        str::from_utf8(&self.buf).unwrap().parse::<T>().unwrap()
    }

    fn vec<T: FromStr>(&mut self, n: usize) -> Vec<T>
        where <T as FromStr>::Err: Debug
    {
        (0..n).map(|_| self.parse()).collect()
    }
}