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.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApplication4
{
    class Program
    {
        static void Main()
        {
            string read = Console.ReadLine();
            string[] split = read.Split(' ');
            int n = Int32.Parse(split[0]);
            int m = Int32.Parse(split[1]);

            read = Console.ReadLine();
            split = read.Split(' ');
            long[] x = new long[n];
            for (int c = 0; c < n; c++)
            {
                x[c] = Int64.Parse(split[c]);
            }
            read = Console.ReadLine();
            split = read.Split(' ');
            long[] y = new long[m];
            for (int c = 0; c < m; c++)
            {
                y[c] = Int64.Parse(split[c]);
            }
            Array.Sort(x);
            Array.Sort(y);
            long juunana = 1000000007;
            long output = 0;


            for (int xstart = 0; xstart < x.Length - 1; xstart++)
                for (int ystart = 0; ystart < y.Length - 1; ystart++)
                    for (int xend = xstart + 1; xend < x.Length; xend++)
                        for (int yend = ystart + 1; yend < y.Length; yend++)
                        {
                            output += (y[yend] - y[ystart]) * (x[xend] - x[xstart]);
                            output = output % juunana;
                        }
            Console.WriteLine(output);

        }


    }
}