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 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include<stdio.h>
#include<stdlib.h>

int main()
{
        int n;
        int m;
        long long x[100000];
        long long y[100000];
        const long long modnum=1000000007;
        int i;
        int j;
        int k;
        int l;
        long long width=0;
        long long height=0;
        long long area=0;

        scanf("%d %d",&n,&m);
        for(i=0;i<n;i++) scanf("%lld",&x[i]);
        for(i=0;i<m;i++) scanf("%lld",&y[i]);

        for(k=0;k<m;k++)
        {
                for(l=k+1;l<m;l++) height+=y[l]-y[k];
                height=height%modnum;
        }

        for(i=0;i<n;i++)
        {
                for(j=i+1;j<n;j++) width+=x[j]-x[i];
                width=width%modnum;
        }
        area=height*width;
        area=area%modnum;
        printf("%lld\n",area);
        return 0;
}