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: Accepted)

using System;
using System.Linq;

namespace ABC058D
{
    class Program
    {
        static void Main(string[] args)
        {
            Solver solver = new Solver();
            solver.Solve();
        }
    }

    class Solver

    {
        private long N;
        private long M;
        private long[] NComb;
        private long[] MComb;
        private long Big;

        public void Solve()
        {
            long[] ints = Console.ReadLine().Split(' ').Select(a => long.Parse(a)).ToArray();
            N = ints[0];
            M = ints[1];
            NComb = new long[N + 1];
            MComb = new long[M + 1];
            setComb();
            Big = (long) Math.Pow(10, 9) + 7;

            long[] x = Console.ReadLine().Split(' ').Select(b => long.Parse(b)).ToArray();
            long[] y = Console.ReadLine().Split(' ').Select(c => long.Parse(c)).ToArray();

            long nLength = 0;

            for (long i = 0; i < N - 1; i++)
            {
                nLength += (x[i + 1] - x[i]) % Big * (NComb[i + 1] % Big);
                nLength %= Big;
            }

            long mLength = 0;

            for (long i = 0; i < M - 1; i++)
            {
                mLength += (y[i + 1] - y[i]) % Big * (MComb[i + 1] % Big);
                mLength %= Big;
            }

            Console.WriteLine(nLength * mLength % Big);
        }

        public void setComb()
        {
            for (long i = 1; i <= N; i++)
            {
                NComb[i] = i * (N - i);
            }

            for (long i = 1; i <= M; i++)
            {
                MComb[i] = i * (M - i);
            }
        }
    }
}