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;
    class Program
    {
        static void Main(string[] args)
        {
            //入力
            string[] xInputMax = Console.ReadLine().Split(' ');
            int xMaxX = int.Parse(xInputMax[0]);
            int xMaxY = int.Parse(xInputMax[1]);
            string[] xInputX = Console.ReadLine().Split(' ');
            int[] x = new int[xMaxX];
            for (int i = 0; i < xMaxX; ++i)
            {
                x[i] = int.Parse(xInputX[i]);
            }
            string[] xInputY = Console.ReadLine().Split(' ');
            int[] y = new int[xMaxY];
            for (int i = 0; i < xMaxY; ++i)
            {
                y[i] = int.Parse(xInputY[i]);
            }
            //計算
            long xOutput = 0;
            for (int i = 0; i < xMaxX - 1; ++i)
            {
                for (int j = i + 1; j <= xMaxX - 1; ++j)
                {
                    for (int k = 0; k < xMaxY - 1; ++k)
                    {
                        for (int l = k + 1; l <= xMaxY - 1; ++l)
                        {
                            long xNewOutput = (((long)x[j] - x[i]) * ((long)y[l] - y[k])) % 1000000007;
                            xOutput = (xOutput + xNewOutput) % 1000000007;
                        }
                    }
                }
            }
            //出力
            Console.WriteLine(xOutput);
        }
    }