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::{BufRead, Write};
use std::io;
use std::ops::{Add, Sub, Mul, Div};
use std::iter::Sum;
use std::cmp::min;

const MOD: u64 = 1000000007;

struct ModInt {
    pub inner: u64,
}

impl From<u64> for ModInt {
    fn from(i: u64) -> ModInt {
        ModInt { inner: i }
    }
}

impl Add<ModInt> for ModInt {
    type Output = ModInt;
    fn add(self, rhs: ModInt) -> ModInt {
        ModInt { inner: (self.inner + rhs.inner) % MOD }
    }
}

impl Sub<ModInt> for ModInt {
    type Output = ModInt;
    fn sub(self, rhs: ModInt) -> ModInt {
        ModInt { inner: (self.inner + MOD - rhs.inner) % MOD }
    }
}

impl Mul<ModInt> for ModInt {
    type Output = ModInt;
    fn mul(self, rhs: ModInt) -> ModInt {
        ModInt { inner: (self.inner * rhs.inner) % MOD }
    }
}

impl Sum for ModInt {
    fn sum<I: Iterator<Item = ModInt>>(iter: I) -> ModInt {
        iter.fold(ModInt::from(0), Add::add)
    }
}

fn solve<R: BufRead, W: Write>(mut input: R, mut output: W) {
    let mut s = String::new();
    input.read_line(&mut s).unwrap();
    let mut split = s.split_whitespace();
    let _ = split.next().unwrap().parse::<u32>().unwrap();
    let _ = split.next().unwrap().parse::<u32>().unwrap();
    let mut s = String::new();
    input.read_line(&mut s).unwrap();
    let x = s.split_whitespace()
        .map(|st| st.parse::<i64>().unwrap())
        .collect::<Vec<_>>();
    s.clear();
    input.read_line(&mut s).unwrap();
    let y = s.split_whitespace()
        .map(|st| st.parse::<i64>().unwrap())
        .collect::<Vec<_>>();
    let x_dist = x.windows(2)
        .map(|v| (v[1] - v[0]) as u64)
        .collect::<Vec<_>>();
    let y_dist = y.windows(2)
        .map(|v| (v[1] - v[0]) as u64)
        .collect::<Vec<_>>();
    writeln!(output,
             "{}",
             ({
                      let len = x_dist.len();
                      (0..len)
                          .map(|i| {
                                   let index = min(i, len - 1 - i);
                                   ModInt::from(x_dist[i]) *
                                   ModInt::from(((len + (len - 2 * index)) * (index + 1) / 2) as
                                                u64)
                               })
                          .sum::<ModInt>()
                  } *
                  {
                      let len = y_dist.len();
                      (0..len)
                          .map(|i| {
                                   let index = min(i, len - 1 - i);
                                   ModInt::from(y_dist[i]) *
                                   ModInt::from(((len + (len - 2 * index)) * (index + 1) / 2) as
                                                u64)
                               })
                          .sum::<ModInt>()
                  })
                 .inner)
            .unwrap();
}

fn main() {
    let stdin = io::stdin();
    let stdout = io::stdout();
    solve(stdin.lock(), stdout.lock());
}

#[cfg(test)]
mod tests {
    fn test(input: &str, output: &str) {
        let mut v = Vec::<u8>::new();
        ::solve(input.as_bytes(), &mut v);
        assert_eq!(String::from_utf8(v).unwrap(), output);
    }
    #[test]
    fn case1() {
        test("3 3
1 3 4
1 3 6\n",
             "60\n");
    }
    #[test]
    fn case2() {
        test("6 5
-790013317 -192321079 95834122 418379342 586260100 802780784
-253230108 193944314 363756450 712662868 735867677\n",
             "835067060\n");
    }
}