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.Collections.Generic;
public class Aprob {
    public static void Main() {
        string[] readSome = new string[2];
        readSome = Console.ReadLine().Split(' ');
        int n = int.Parse(readSome[0]);
        int m = int.Parse(readSome[1]);
        readSome = new string[n];
        readSome = Console.ReadLine().Split(' ');
        int[] x = new int[n];
        for (int i = 0; i < n; i++) {
            x[i] = int.Parse(readSome[i]);
        }
        readSome = new string[m];
        readSome = Console.ReadLine().Split(' ');
        int[] y = new int[m];
        for (int i = 0; i < m; i++) {
            y[i] = int.Parse(readSome[i]);
        }
        //int conbix = Conbi(n);
        List<long> distXX = new List<long>();
        //long[] distX = new long[conbix];
        int countx = 0;
        for (int i = 0; i < n-1; i++) {
            for (int j = i + 1; j < n; j++) {
                distXX.Add((x[j] - x[i]) % ((int)Math.Pow(10, 9) + 7));
                //distX[count] = (x[j] - x[i]) % ((int)Math.Pow(10, 9) + 7);
                countx++;
            }
        }
        int county = 0;
        //int conbiY = Conbi(m);
        List<long> distYY = new List<long>();
        //long[] distY = new long[conbiY];
        for (int i = 0; i < m - 1; i++) {
            for (int j = i + 1; j < m; j++) {
                distYY.Add((y[j] - y[i]) % ((int)Math.Pow(10, 9) + 7));
                //distY[count] = (y[j] - y[i]) % ((int)Math.Pow(10, 9) + 7);
                county++;
            }
        }
        long area = 0;
        for (int i = 0; i < countx; i++) {
            for (int j = 0; j < county; j++) {
                //Console.WriteLine(distX[i]+"*"+distY[j]);
                area += (distXX[i] * distYY[j]) % ((int)Math.Pow(10, 9) + 7);
            }
            area %= ((int)Math.Pow(10, 9) + 7);
        }
        Console.WriteLine(area);

    }

    public static int Conbi(int n) {
        int conbi = 1;
        if (n != 2) {
            for (int i = 1; i <= n; i++) {
                conbi *= i;
            }
            for (int i = 1; i <= n - 2; i++) {
                conbi /= i;
            }
            conbi /= 2;
        } else if (n == 2) {
            conbi = 1;
        } else {
            conbi = 0;
        }
        return conbi;
    }
}