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Contest: Task: Related: TaskA TaskC

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:

sample1-1

The total area of the nine rectangles A, B, ..., I shown in the following figure, is $60$.

sample1-2

Sample Input 2

6 5
-790013317 -192321079 95834122 418379342 586260100 802780784
-253230108 193944314 363756450 712662868 735867677

Sample Output 2

835067060