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: Time Limit Exceeded)

using System;
using System.Linq;
using System.IO;
using System.Text;
using System.Collections;
using System.Collections.Generic;
using System.Text.RegularExpressions;
//using System.Numerics;
 
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]);
        long[] x = Console.ReadLine().Split(' ')
                        .Select(long.Parse)
                        .OrderBy(elem => elem)
                        .ToArray();
        long[] y = Console.ReadLine().Split(' ')
                        .Select(long.Parse)
                        .OrderBy(elem => elem)
                        .ToArray();

        long totalArea = 0;
        for (int i = 1; i < n; i++)
        {
            for (int j = 1; j < m; j++)
            {
                long area = 0;
                //Console.Error.WriteLine("i: {0}, j:{1}", i, j);
                //Console.Error.WriteLine("x[i] - x[i - 1] = {0} - {1} = {2}", x[i], x[i - 1], x[i] - x[i - 1]);
                //Console.Error.WriteLine("y[j] - y[j - 1] = {0} - {1} = {2}", y[j], y[j - 1], y[j] - y[j - 1]);
                area = (x[i] - x[i - 1]) * (y[j] - y[j - 1]) % Divisor;
                //Console.Error.WriteLine("area = {0}", area);
                area = area * i * (n - i) % Divisor;
                //Console.Error.WriteLine(" * {0}", i * (n - i));
                area = area * j * (m - j) % Divisor;
                //Console.Error.WriteLine(" * {0}", j * (m - j));
                //Console.Error.WriteLine("totalArea = {0} + {1} = ", totalArea, area);
                totalArea = (totalArea + area) % Divisor;
                //Console.Error.WriteLine("{0}", totalArea);
            }
        }
        
        Console.WriteLine(totalArea);
    }
}