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 Common Lisp (SBCL 1.1.14) (judge verdict: Time Limit Exceeded)

(defun split-with (string &key (delimiterp #'(lambda (c) (char= c #\Space))))
  (loop :for beg = (position-if-not delimiterp string)
        :then (position-if-not delimiterp string :start (1+ end))
        :for end = (and beg (position-if delimiterp string :start beg))
        :when beg :collect (subseq string beg end)
        :while end))

(destructuring-bind (n m) (mapcar #'parse-integer (split-with (read-line)))

  (let* ((a (- n 1))
         (b (- m 1))
         (xs (make-array n :initial-contents
                         (mapcar #'parse-integer (split-with (read-line)))))
         (ys (make-array m :initial-contents
                         (mapcar #'parse-integer (split-with (read-line)))))
         (hor (make-array a :initial-contents
                          (loop :for i :from 0 :below (- n 1)
                                :collect (- (aref xs (+ i 1)) (aref xs i)))))
         (ver (make-array b :initial-contents
                          (loop :for j :from 0 :below (- m 1)
                                :collect (- (aref ys (+ j 1)) (aref ys j)))))
         (sum 0))
    (loop :for xcell :from 1 :to a
          :do (loop :for xoffset :from 0 :to (- a xcell)
                    :for xlen = (loop :for i :from 0 :below xcell
                                      :summing (aref hor (+ xoffset i)))
                    :do (loop :for ycell :from 1 :to b
                              :do (loop :for yoffset :from 0 :to (- b ycell)
                                        :for ylen = (loop :for j :from 0 :below ycell
                                                          :summing (aref ver (+ yoffset j)))
                                        :do (setf sum (mod (+ sum (* xlen ylen)) 1000000007))))))
  (format t "~d~%" sum)))