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.IO;
using System.Linq;
using System.Collections.Generic;
using static System.Math;

class P
{
    static void Main()
    {
        int[] nm = Console.ReadLine().Split().Select(int.Parse).ToArray();
        int n = nm[0];
        int m = nm[1];
        int[] x = Console.ReadLine().Split().Select(int.Parse).ToArray();
        int[] y = Console.ReadLine().Split().Select(int.Parse).ToArray();
        //長方形に含まれる回数が欲しい
        long xSum = 0;
        for (int i = 0; i < n - 1; i++)
        {
            long sum = 0;
            for (int j = 0; j < n - i - 1; j++)
            {
                sum += x[i + j + 1] - x[i + j];
                sum %= 1000000007;
                xSum += sum;
                xSum %= 1000000007;
            }
        }
        long ySum = 0;
        for (int i = 0; i < m - 1; i++)
        {
            long sum = 0;
            for (int j = 0; j < m - i - 1; j++)
            {
                sum += y[i + j + 1] - y[i + j];
                sum %= 1000000007;
                ySum += sum;
                ySum %= 1000000007;
            }
        }
        Console.WriteLine((xSum * ySum) % 1000000007);
    }
}