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 $10^9+7$.