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: Accepted)

import java.io.BufferedReader;
import java.io.InputStreamReader;

public class Main {
	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] sa = br.readLine().split(" ");
		int n = Integer.parseInt(sa[0]);
		int m = Integer.parseInt(sa[1]);
		sa = br.readLine().split(" ");
		long[] x = new long[n];
		for (int i = 0; i < n; i++) {
			x[i] = Integer.parseInt(sa[i]);
		}
		sa = br.readLine().split(" ");
		long[] y = new long[m];
		for (int i = 0; i < m; i++) {
			y[i] = Integer.parseInt(sa[i]);
		}
		br.close();

		int mod = 1000000007;
		long xx = 0;
		for (int i = 0; i < n; i++) {
			xx += i * x[i] - (n - i - 1) * x[i];
			xx %= mod;
		}
		long yy = 0;
		for (int i = 0; i < m; i++) {
			yy += i * y[i] - (m - i - 1) * y[i];
			yy %= mod;
		}
		long ans = xx * yy % mod;
		if (ans < 0) {
			ans += mod;
		}
		System.out.println(ans);
	}
}