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 Scala (2.13.1) (judge verdict: Accepted)

object Main extends App {
  val sc = new java.util.Scanner(System.in)
  val n, m = sc.nextInt()
  val x = List.fill(n)(sc.nextLong())
  val y = List.fill(m)(sc.nextLong())

  val mod = 1000000007

  def plus(a: Long, b: Long): Long = (a + b) % mod
  def minus(a: Long, b: Long): Long = (a - b + mod) % mod
  def times(a: Long, b: Long): Long = (a * b) % mod

  val c = x.sliding(2).map{
    case List(x1, x2) => x2 - x1
  }.zipWithIndex.map{
    case (e, idx) => times(times(e, idx+1), n-idx-1)
  }.reduceLeft(plus)

  val d = y.sliding(2).map{
    case List(y1, y2) => y2 - y1
  }.zipWithIndex.map{
    case (e, idx) => times(times(e, idx+1), m-idx-1)
  }.reduceLeft(plus)

  println(times(c, d))
}