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.Linq;
using System.Numerics;
using System.Collections.Generic;
using System.Text;
using System.Threading.Tasks;
using System.IO;
using System.Diagnostics;
using System.Text.RegularExpressions;
using static System.Console;

namespace CsTest
{
    class Program
    {
        static void Main()
        {
            long[] nm = AtCoder.ReadInt64Array();
            var n = nm[0];
            var m = nm[1];
            int[] x = AtCoder.ReadInt32Array();
            int[] y = AtCoder.ReadInt32Array();

            var result = new BigInteger();

            for (int xi = 0; xi < n - 1; xi++) for (int yi = 0; yi < m - 1; yi++)
                {
                    var hidariuekazu = (xi + 1) * (yi + 1);
                    var migisitakazu = (x.Length - xi - 1) * (y.Length - yi - 1);
                    result += BigInteger.Multiply((x[xi + 1] - x[xi]), (y[yi + 1] - y[yi])) * hidariuekazu * migisitakazu;
                }


            WriteLine(result % 1000000007);
        }
    }

    public class AtCoder
    {
        public static int ReadInt32() => int.Parse(ReadLine());
        public static string[] ReadStringArray() => ReadLine().Split(Array.Empty<char>(), StringSplitOptions.RemoveEmptyEntries);
        public static int[] ReadInt32Array() => ReadStringArray().Select(s => int.Parse(s)).ToArray();
        public static long[] ReadInt64Array() => ReadStringArray().Select(s => long.Parse(s)).ToArray();
    }
    public static class PermutationsAndCombinations
    {
        public static long nCr(int n, int r)
        {
            // naive: return Factorial(n) / Factorial(r) * Factorial(n - r);
            return n - 2 * r < 0? nCr(n, n - r) : nPr(n, r) / Factorial(r);
        }

        public static long nPr(int n, int r)
        {
            // naive: return Factorial(n) / Factorial(n - r);
            return FactorialDivision(n, n - r);
        }

        private static long FactorialDivision(int topFactorial, int divisorFactorial)
        {
            long result = 1;
            for (int i = topFactorial; i > divisorFactorial; i--)
                result *= i;
            return result;
        }

        private static long Factorial(int i)
        {
            if (i <= 1)
                return 1;
            return i * Factorial(i - 1);
        }
    }
}