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 Data.Int
modNum = 1000000007
toInt64 :: Int -> Int64
toInt64 = (fromInteger :: Integer -> Int64) . toInteger

main = do
  nm <- map (read :: String -> Int64) . words <$> getLine
  inputX <- map (read :: String -> Int64) . words <$> getLine
  inputY <- map (read :: String -> Int64) . words <$> getLine
  putStrLn . show $ solve' ((head nm) - 1) ((last nm) - 1) inputX inputY

solve' :: Int64 -> Int64 -> [Int64] -> [Int64] -> Int64
solve' n m x y = if m > 2 then flip mod modNum $ solve n m x y + solve' n (m-2) x (tail . init $ y)
                          else solve n m x y

solve :: Int64 -> Int64 -> [Int64] -> [Int64] -> Int64
solve n m x y = let xx = (last x) - (head x)
                    yy = (last y) - (head y)
                    area = flip mod modNum $ (flip mod modNum $ n * m) * (flip mod modNum $ xx * yy)
                    in if n > 2 then flip mod modNum $ area + solve (n-2) m (tail . init $ x) y
                            else area