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)

#[allow(unused_imports)]
use std::cmp::{Ordering};

#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};

#[allow(unused_imports)]
use std::io::{stdin, stdout, BufWriter, Write};

#[allow(unused_imports)]
use std::iter::FromIterator;

#[allow(unused_macros)]
macro_rules! min {
    ($x: expr) => ($x);
    ($x: expr, $($z: expr),+) => {{
        std::cmp::min($x, min!($($z),*))
    }}
}

#[allow(unused_macros)]
macro_rules! max {
    ($x: expr) => ($x);
    ($x: expr, $($z: expr),+) => {{
        std::cmp::max($x, max!($($z),*))
    }}
}

#[allow(unused_macros)]
macro_rules! get { 
    ([$t: ty]) => { 
        { 
            let mut line = String::new(); 
            stdin().read_line(&mut line).unwrap(); 
            line.split_whitespace().map(|t|t.parse::<$t>().unwrap()).collect::<Vec<_>>()
        }
    };
    ([$t: ty];$n: expr) => {
        (0..$n).map(|_|get!([$t])).collect::<Vec<_>>()
    };
    ($t: ty) => {
        {
            let mut line = String::new();
            stdin().read_line(&mut line).unwrap();
            line.trim().parse::<$t>().unwrap()
        }
    };
    ($($t: ty),*) => {
        { 
            let mut line = String::new();
            stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            ($(iter.next().unwrap().parse::<$t>().unwrap(),)*)
        }
    };
    ($t: ty; $n: expr) => {
        (0..$n).map(|_|get!($t)).collect::<Vec<_>>()
    };
    ($($t: ty),*; $n: expr) => {
        (0..$n).map(|_|get!($($t),*)).collect::<Vec<_>>()
    };
}

#[allow(unused_macros)]
macro_rules! debug {
    ($($a:expr),*) => {
        #[cfg(debug_assertions)]
        writeln!(&mut std::io::stderr(), concat!("[DEBUG] ", $(stringify!($a), "={:?} "),*), $($a),*).unwrap();
    }
}

const BIG_STACK_SIZE: bool = true;

#[allow(dead_code)]
fn main() {
    use std::thread;
    if BIG_STACK_SIZE {
        thread::Builder::new()
            .stack_size(32 * 1024 * 1024)
            .name("solve".into())
            .spawn(solve)
            .unwrap()
            .join()
            .unwrap();
    } else {
        solve();
    }
}

use self::modint::ModInt;
mod modint {
    use std;
#[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord)]
    pub struct ModInt(usize);
    impl ModInt {
        pub fn new(value: usize) -> Self {
            ModInt(value)
        }
        fn modulo() -> usize {
            1_000_000_007
        }
    }
    impl std::ops::Add for ModInt {
        type Output = Self;
        fn add(self, other: Self) -> Self {
            let mut value = self.0 + other.0;
            if value > Self::modulo() {
                value -= Self::modulo();
            }
            ModInt(value)
        }
    }
    impl std::ops::Add<usize> for ModInt {
        type Output = Self;
        fn add(self, other: usize) -> Self {
            let mut value = self.0 + other;
            if value > Self::modulo() {
                value -= Self::modulo();
            }
            ModInt(value)
        }
    }
    impl std::ops::Sub for ModInt {
        type Output = Self;
        fn sub(self, other: Self) -> Self {
            let mut value = self.0;
            if value < other.0 {
                value += Self::modulo();
            }
            value -= other.0;
            ModInt(value)
        }
    }
    impl std::ops::Sub<usize> for ModInt {
        type Output = Self;
        fn sub(self, other: usize) -> Self {
            let mut value = self.0;
            if value < other {
                value += Self::modulo();
            }
            value -= other;
            ModInt(value)
        }
    }
    impl std::ops::Mul for ModInt {
        type Output = Self;
        fn mul(self, other: Self) -> Self {
            let value = self.0 * other.0 % Self::modulo();
            ModInt(value)
        }
    }
    impl std::ops::Mul<usize> for ModInt {
        type Output = Self;
        fn mul(self, other: usize) -> Self {
            let value = self.0 * other % Self::modulo();
            ModInt(value)
        }
    }
    impl std::ops::Div for ModInt {
        type Output = Self;
        fn div(self, other: Self) -> Self {
            let mut exp = Self::modulo() - 2;
            let mut value = self.0;
            let mut ovalue = other.0;
            while exp > 0 {
                if exp % 2 == 1 {
                    value = value * ovalue % Self::modulo();
                }
                ovalue = ovalue * ovalue % Self::modulo();
                exp /= 2;
            }
            ModInt(value)
        }
    }
    impl std::ops::Div<usize> for ModInt {
        type Output = Self;
        fn div(self, other: usize) -> Self {
            let mut exp = Self::modulo() - 2;
            let mut value = self.0;
            let mut ovalue = other;
            while exp > 0 {
                if exp % 2 == 1 {
                    value = value * ovalue % Self::modulo();
                }
                ovalue = ovalue * ovalue % Self::modulo();
                exp /= 2;
            }
            ModInt(value)
        }
    }
    impl std::ops::AddAssign for ModInt {
        fn add_assign(&mut self, other: Self) {
            *self = *self + other;
        }
    }
    impl std::ops::AddAssign<usize> for ModInt {
        fn add_assign(&mut self, other: usize) {
            *self = *self + other;
        }
    }
    impl std::ops::SubAssign for ModInt {
        fn sub_assign(&mut self, other: Self) {
            *self = *self - other;
        }
    }
    impl std::ops::SubAssign<usize> for ModInt {
        fn sub_assign(&mut self, other: usize) {
            *self = *self - other;
        }
    }
    impl std::ops::MulAssign for ModInt {
        fn mul_assign(&mut self, other: Self) {
            *self = *self * other;
        }
    }
    impl std::ops::MulAssign<usize> for ModInt {
        fn mul_assign(&mut self, other: usize) {
            *self = *self * other;
        }
    }
    impl std::ops::DivAssign for ModInt {
        fn div_assign(&mut self, other: Self) {
            *self = *self / other;
        }
    }
    impl std::ops::DivAssign<usize> for ModInt {
        fn div_assign(&mut self, other: usize) {
            *self = *self / other;
        }
    }
    impl std::fmt::Debug for ModInt {
        fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
            write!(f, "{}", self.0)
        }
    }
    impl std::fmt::Display for ModInt {
        fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
            write!(f, "{}", self.0)
        }
    }
}

const MOD: isize = 1_000_000_007;

fn solve() {
    let (n,m) = get!(usize, usize);
    let x = get!([isize]);
    let y = get!([isize]);

    let mut x_sum = ModInt::new(0);
    let mut y_sum = ModInt::new(0);

    for i in 0..n {
        let tmp = ModInt::new(2*i+1) - ModInt::new(n);
        let xt = if x[i] < 0 {
            ModInt::new((x[i]+MOD) as usize)
        } else {
            ModInt::new(x[i] as usize)
        };
        x_sum += tmp*xt;
    }
    for i in 0..m {
        let tmp = ModInt::new(2*i+1) - ModInt::new(m);
        let yt = if y[i] < 0 {
            ModInt::new((y[i]+MOD) as usize)
        } else {
            ModInt::new(y[i] as usize)
        };
        y_sum += tmp*yt;
    }
    println!("{}", x_sum*y_sum);
}