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 Ruby (2.3.3) (judge verdict: Accepted)

DIVISOR = 10**9+7
N, M = gets.split(" ").first(2).map(&:to_i)
Xa = gets.split(" ").first(N).map(&:to_i).reverse
Ya = gets.split(" ").first(M).map(&:to_i).reverse

widths = (0..Xa.size-2).map{|i| Xa[i] - Xa[i+1] }
heights = (0..Ya.size-2).map{|i| Ya[i] - Ya[i+1] }
total_width = widths.map.with_index{|w, i|
  w * (i + 1) * (widths.size-i)
}.inject(0, :+)
total_height = heights.map.with_index{|h, i|
  h * (i + 1) * (heights.size-i)
}.inject(0, :+)

puts total_width * total_height % DIVISOR