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;

namespace _058
{
    class Program
    {
        // 058-D
        static void Main(string[] args)
        {
            var line = Console.ReadLine().Split(' ').Select(a => long.Parse(a)).ToArray();
            long n = line[0];
            long m = line[1];
            var x = Console.ReadLine().Split(' ').Select(a => long.Parse(a)).ToArray();
            var y = Console.ReadLine().Split(' ').Select(a => long.Parse(a)).ToArray();

            long s = 0;
            long s1 = 0;
            long s2 = 0;
            for (long j = 1; j <= n; j++)
            {
                for (long i = 1; i < j; i++)
                {
                    s1 += x[j - 1] - x[i - 1];
                    s1 = s1 % ((long)Math.Pow(10, 9) + 7);
                }
            }
            for (long l = 1; l <= m; l++)
            {
                for (long k = 1; k < l; k++)
                {
                    s2 += (y[l - 1] - y[k - 1]);
                    s2 = s2 % ((long)Math.Pow(10, 9) + 7);
                }
            }
            s = (s1*s2) % ((long)Math.Pow(10, 9) + 7);
            Console.WriteLine(s);
        }
    }
}