Field#8597
On a two-dimensional plane, there are lines drawn parallel to the axis, and lines drawn parallel to the axis. Among the lines parallel to the axis, the -th from the bottom is represented by y = y_i. Similarly, among the lines parallel to the axis, the -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.
The first line contains two integers and (2 \leq n, m \leq 10^5).
The second line contains integers -10^9 \leq x_1 < x_2 < \ldots < x_n \leq 10^9.
The third line contains integers -10^9 \leq y_1 < y_2 < \ldots < y_m \leq 10^9.
Print the total area of the rectangles, modulo 10^9 + 7.
The following figure illustrates this input:
The total area of the nine rectangles , , ..., shown in the following figure, is .
Example 1
Example 2