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 Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

import Control.Applicative
import Data.Array.IArray

main = do
  (n:m:_) <- (map read) . words <$> getLine
  xs <- (map (read::String->Integer)) . words <$> getLine
  ys <- (map (read::String->Integer)) . words <$> getLine

  let
    xs' = array (0,n) ((0,sum xs) : [(i, f $ xs'!(i-1) - xs!!(i-1)) | i<-[1..n] ]) :: Array Int Integer
    ys' = array (0,m) ((0,sum ys) : [(i, f $ ys'!(i-1) - ys!!(i-1)) | i<-[1..m] ]) :: Array Int Integer

  let x = g [xs'!(i+1) - (fromIntegral (n - (i+1))) * (xs!!i) | i<-[0..n-1]]
  let y = g [ys'!(i+1) - (fromIntegral (m - (i+1))) * (ys!!i) | i<-[0..m-1]]

  print $ mod (x * y) (10^9+7)
  where
    f n = mod n (10^9+7)
    g [] = 0
    g (x:xs) = f $ x + g xs