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: Accepted)

#include <stdio.h>

#define MOD (1000000007UL)

unsigned long total(int n)
{
    unsigned long total_x = 0;
    int prev_x;
    for (int i = 0; i < n; i++){
        int x;
        scanf("%d", &x);
        if (i == 0){
            prev_x = x;
        } else {
            int g = (i <= n/2) ? i : n - i;
            total_x += (unsigned long)(x - prev_x) * (unsigned long)g * (unsigned long)(n - g);
            total_x %= MOD;
            prev_x = x;
        }
    }
    return total_x;
}

int main(void)
{
    int n,m;
    scanf("%d %d", &n, &m);

    unsigned long total_x = total(n);
    unsigned long total_y = total(m);

    printf("%lu", (total_x * total_y) % MOD);

    return 0;
}