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)

Mod = 10**9 + 7
N,M = gets.split.map &:to_i
X = gets.split.map &:to_i
Y = gets.split.map &:to_i

def ar(xs)
  dx = (1...xs.size).map{ |i| xs[i] - xs[i-1] }
  sx = [0]
  ax = 0
  (0...dx.size).each{ |i| 
    sx << (sx[-1] + dx[i]) % Mod
  }
  ssx = [0]
  (1...sx.size).each{ |i| 
    ssx << (ssx[-1] + sx[i]) % Mod
    v = i*sx[i] % Mod
    v = (v - ssx[-2] + Mod) % Mod
    ax = (ax + v) % Mod
  }
  ax
end
  
p ar(X) * ar(Y) % Mod