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: Wrong Answer)

require 'prime'
include Math
def max(a,b);                    a > b ? a : b                            end
def min(a,b);                    a < b ?  a : b                           end
def swap(a,b);                   a, b = b, a                              end
def gif;                         gets.to_i                                end
def gsf;                         gets.chomp                               end
def gi;                          gets.split.map(&:to_i)                   end
def gs;                          gets.chomp.split.map(&:to_s)             end
def gc;                          gets.chomp.split('')                     end
def pr(num);                     num.prime_division                       end
def putall(obj);                 obj.each{|o| puts(o)}                    end
def array(size,init=nil);        Array.new(size){init}                    end
def darray(size1,size2,init=nil);Array.new(size1){Array.new(size2){init}} end
def rep(num);                    num.times {|i|yield(i)}                  end
def repl(st,en);                 st.upto(en) {|i|yield(i)}                end


n,m = gi
x = gi
y = gi
hx = []
 rep x.size-1 do |i|
 	hx << x[i+1]-x[i]
 end
hy = []
 rep y.size-1 do |i|
 	hy << y[i+1]-y[i]
 end

s = 0
hx.each do |xx|
	hy.each do |yy|
		s += xx*yy*(2**(x.size+y.size-4))
	end
end

puts s % ((10**9) + 7)