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 (2.11.7) (judge verdict: Accepted)

import io.StdIn.readLine
object Main extends App {
  val mod = 1000000007
  val Array(n, m) = readLine.split(" ").map(_.toInt)
  val xs = readLine.split(" ").toSeq.map(_.toLong)
  val ys = readLine.split(" ").toSeq.map(_.toLong)
  val lx = (for (i <- 0 until n) yield xs(i) * (2 * i - n + 1)).reduce((a, b) => (a + b) % mod)
  val ly = (for (j <- 0 until m) yield ys(j) * (2 * j - m + 1)).reduce((a, b) => (a + b) % mod)
  println(lx * ly % mod)
}