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;

public class Program
{

    public void Proc()
    {
        int[] inpt = Reader.ReadLine().Split(' ').Select(a => int.Parse(a)).ToArray();
        this.xList = Reader.ReadLine().Split(' ').Select(a => long.Parse(a)).ToArray();
        this.yList = Reader.ReadLine().Split(' ').Select(a => long.Parse(a)).ToArray();

        long ans = 0;
        long mod = 1000000000 + 7;
        for (int i = 0; i < xList.Length - 1; i++) {
            long mulLeft = i + 1;
            long mulRight = xList.Length - i - 1;
			for (int j = 0; j < yList.Length - 1; j++) {
                long menseki = (xList[i + 1] - xList[i]) * (yList[j + 1] - yList[j]) % mod;
                long mulUp = j + 1;
                long mulDown = yList.Length - j - 1;
                long mul = mulLeft * mulRight % mod;
                mul = mul * mulUp % mod;
                mul = mul * mulDown % mod;
                menseki = menseki * mul % mod;
                ans += menseki;
                ans = ans % mod;
            }
        }
        Console.WriteLine(ans);
    }

    private long[] xList;
    private long[] yList;


    public class Reader
	{
		private static StringReader sr;
		public static bool IsDebug = false;
		public static string ReadLine()
		{
			if (IsDebug)
			{
				if (sr == null)
				{
					sr = new StringReader(InputText.Trim());
				}
				return sr.ReadLine();
			}
			else
			{
				return Console.ReadLine();
			}
		}
		private static string InputText = @"


6 5
-790013317 -192321079 95834122 418379342 586260100 802780784
-253230108 193944314 363756450 712662868 735867677


";
	}

	public static void Main(string[] args)
	{
#if DEBUG
		Reader.IsDebug = true;
#endif
		Program prg = new Program();
		prg.Proc();
	}
}