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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;
using System.IO;
using System.Text;
using System.Collections;
using System.Collections.Generic;
using System.Text.RegularExpressions;
 
class Program
{
    static void Main()
    {
        const long Divisor = 1000000007;
        string[] inputs = Console.ReadLine().Split(' ');
        int n = int.Parse(inputs[0]);
        int m = int.Parse(inputs[1]);
        int[] x = Console.ReadLine().Split(' ')
                        .Select(int.Parse)
                        .OrderBy(elem => elem)
                        .ToArray();
        int[] y = Console.ReadLine().Split(' ')
                        .Select(int.Parse)
                        .OrderBy(elem => elem)
                        .ToArray();

        long totalArea = 0, areaX = 0, areaY = 0;
        for (int i = 1; i < n; i++)
        {
            areaX += (long)(x[i] - x[i - 1]) * i % Divisor * (n - i) % Divisor;
            areaX %= Divisor;
        }
        for (int i = 1; i < m; i++)
        {
            areaY += (long)(y[i] - y[i - 1]) * i % Divisor * (m - i) % Divisor;
            areaY %= Divisor;
        }
        totalArea = areaX * areaY % Divisor;
        
        Console.WriteLine(totalArea);
    }
}