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;

namespace arc071_b
{
	class Program
	{
		static void Main(string[] args)
		{
			int[] x = Console.ReadLine().Split().Select(int.Parse).ToArray();
			long[] a = Console.ReadLine().Split().Select(long.Parse).ToArray();
			long[] b = Console.ReadLine().Split().Select(long.Parse).ToArray();
			long ret = 0; long mod = (long)Math.Pow(10, 9) + 7;
			for (int i = 1; i < x[0]; i++)
			{
				for (int j = 1; j < x[1]; j++)
				{
					long now = a[i] - a[i - 1];
					now *= b[j] - b[j - 1]; now %= mod;
					now *= i; now %= mod;
					now *= (x[0] - i); now %= mod;
					now *= j; now %= mod;
					now *= (x[1] - j); now %= mod;
					ret += now;ret %= mod;
				}
			}
			Console.WriteLine(ret);
		}
	}
}