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.Collections.Generic;

public class Program
{
    public static void Main()
    {
        var size = Console.ReadLine().Split()
            .Select(x => int.Parse(x))
            .ToArray();
        var linesQuery =
            from _ in Enumerable.Range(0, 2)
            select Console.ReadLine().Split()
                .Select(x => long.Parse(x))
                .ToArray();
        var lines = linesQuery.ToArray();
        
        const long mod = (long)(1e9 + 7);

        var total = new long[2];
        for (int a = 0; a < 2; ++a)
        {
            for (int i = 0; i < size[a]; ++i)
            {
                total[a] += (2 * i - size[a] + 1) * lines[a][i];
            }

            total[a] %= mod;
        }

        Console.WriteLine(total[0] * total[1] % mod);
    }
}