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)

{-# LANGUAGE TupleSections #-}

main :: IO ()
main = do
    _ <- getLine
    xs <- getInts
    ys <- getInts
    print $ solve xs ys

solve :: [Int] -> [Int] -> Int
solve xs ys = getSum . foldMap (Sum . calc) $ pair (choise xs) (choise ys)

choise :: [Int] -> [Pair]
choise [] = []
choise [x] = []
choise (x:xs) = [(x,x') | x' <- xs] ++ choise xs

pair :: [a] -> [a] -> [(a,a)]
pair xs = foldr (\y a -> map (,y) xs ++ a) []

calc :: (Pair,Pair) -> Int
calc (xs,ys) = dist xs * dist ys
    where dist (a,b) = abs (a-b)

type Pair = (Int, Int)

newtype Sum = Sum { getSum :: Int }

instance Monoid Sum where
    mempty = Sum 0
    mappend (Sum x) (Sum y) = Sum $ (x+y) `mod` lim

lim :: Int
lim = 7 + 10^9

getInts :: IO [Int]
getInts = map read . words <$> getLine