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.Arrays;
import java.util.Scanner;

public class Main{

	public static void main(String[] args) {
		// TODO 自動生成されたメソッド・スタブ
		Scanner scan = new Scanner(System.in);
		int n=scan.nextInt();
		int m=scan.nextInt();
		int[] x = new int[n];
		int[] y=new int[m];
		long[] xl=new long[n];
		long[] yl=new long[m];


		for(int i=0;i<n;i++){
			x[i]=scan.nextInt();
		}
		Arrays.sort(x);
		for(int i=0;i<n-1;i++){
			xl[i]=x[i+1]-x[i];
		}
		for(int i=0;i<m;i++){
			y[i]=scan.nextInt();
		}
		Arrays.sort(y);
		for(int i=0;i<m-1;i++){
			yl[i]=y[i+1]-y[i];
		}


		long sum=0;
		long ans=0;

		for(int i=0;i<n-1;i++){
			for(int j=0;j<m-1;j++){
				sum=((xl[i]%1000000007)*(yl[j]%1000000007))%1000000007*(i+1)*(j+1)*(n-i-1)*(m-j-1)%(1000000007);
				ans=(ans+sum)%(1000000007);
			}
		}


		System.out.println(ans);
	}

}