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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;
using static System.Console;
using System.Text;
using System.IO;
using static System.Math;
using System.Numerics;

namespace AtCoder
{
    class Program
    {
        static public long[] Sarray() { return ReadLine().Split().Select(long.Parse).ToArray(); }
        static public List<long> Slist() { return ReadLine().Split().Select(long.Parse).ToList(); }
        static long Mod = (long)1e9 + 7;
        static void Main(string[] args)
        {
            //SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
            Solve();
            //Out.Flush();
            Read();
        }
        static void Solve()
        {
            var NM = Sarray();
            var N = NM[0];
            var M = NM[1];
            var Xi = Sarray();
            var Yi = Sarray();
            Array.Sort(Xi);
            Array.Sort(Yi);
            var dstX = new long[N - 1];
            for (var i = 0; i < N - 1; ++i)
                dstX[i] = Xi[i + 1] - Xi[i];
            var dstY = new long[M - 1];
            for (var i = 0; i < M - 1; ++i)
                dstY[i] = Yi[i + 1] - Yi[i];

            var sumX = 0L;
            var W = N - 1;
            for (var i = 1; i <= W; ++i)
            {
                var t = i * (W - i + 1) % Mod * dstX[i - 1] % Mod;
                sumX = (sumX + t) % Mod;
            }
            var sumY = 0L;
            var H = M - 1;
            for (var i = 1; i <= H; ++i)
            {
                var t = i * (H - i + 1) % Mod * dstY[i - 1] % Mod;
                sumY = (sumY + t) % Mod;
            }
            WriteLine(sumX * sumY % Mod);
        }
    }
}