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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.Scanner;

public class Main {
    public static long D = 1000000007;

    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int m = sc.nextInt();
        int[] xs = new int[n];
        int[] ys = new int[m];
        for (int i = 0; i < n; i++) {
            xs[i] = sc.nextInt();
        }
        for (int i = 0; i < m; i++) {
            ys[i] = sc.nextInt();
        }
        int nn = n - 1;
        int mm = m - 1;
        long[] dxs = new long[nn];
        long[] dys = new long[mm];
        for (int i = 0; i < nn; i++) {
            dxs[i] = (xs[i + 1] - xs[i]) % D;
        }
        for (int i = 0; i < mm; i++) {
            dys[i] = (ys[i + 1] - ys[i]) % D;
        }

        long sum = 0;
        for (int i = 0; i < n - 1; i++) {
            for (int j = 0; j < m - 1; j++) {
                long area = (dxs[i] * dys[j]) % D;
                long count = count(n, m, i, j);
                sum += area * count;
                sum = sum % D;
            }
        }

        System.out.println(sum);
    }

    public static long count(long n, long m, long i, long j) {
        long x = ((i + 1) * (n - (i + 1))) % D;
        long y = ((j + 1) * (m - (j + 1))) % D;
        return x * y;
    }
}