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 (Clang 3.8.0) (judge verdict: Runtime Error)

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

int main(void) {
    int n, m, i, x_offset, y_offset, tmp;
    int *x_freq, *y_freq;
    long long *x, *y, **area, sum = 0;
    scanf("%d %d", &n, &m);
    x = malloc(n * sizeof(long long));
    x_freq = malloc(n * sizeof(int));
    y = malloc(m * sizeof(long long));
    y_freq = malloc(n * sizeof(int));
    area = malloc(n * sizeof(long long *));

    for (i = 0; i < n; i++) {
        area[i] = malloc(m * sizeof(long long));
    }
    for (i = 0; i < n; i++) {
        scanf("%lld", &x[i]);
    }
    for (i = 0; i < m; i++) {
        scanf("%lld", &y[i]);
    }

    for (x_offset = 0; x_offset < n - 1; x_offset++) {
        for (y_offset = 0; y_offset < m - 1; y_offset++) {
            area[x_offset][y_offset] = (x[x_offset + 1] - x[x_offset]) * (y[y_offset + 1] - y[y_offset]);
        }
    }

    x_freq[0] = x_freq[n - 2] = n - 1;
    tmp = n - 1;
    for (i = 1; i < (n - 1) / 2; i++) {
        tmp -= 2;
        x_freq[i] = x_freq[n - i - 2] = x_freq[i - 1] + tmp;
    }
    if ((n - 1) % 2) {
        x_freq[n / 2 - 1] = x_freq[n / 2] + 1;
    }
    y_freq[0] = y_freq[m - 2] = m - 1;
    tmp = m - 1;
    for (i = 1; i < (m - 1) / 2; i++) {
        tmp -= 2;
        y_freq[i] = y_freq[m - i - 2] = y_freq[i - 1] + tmp;
    }
    if ((m - 1) % 2) {
        y_freq[m / 2 - 1] = y_freq[m / 2] + 1;
    }

    for (x_offset = 0; x_offset < n - 1; x_offset++) {
        for (y_offset = 0; y_offset < m - 1; y_offset++) {
            sum += area[x_offset][y_offset] * x_freq[x_offset] * y_freq[y_offset];
            sum = sum % 1000000007;
        }
    }

    printf("%lld\n", sum);
    return 0;
}