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 Python (3.4.3) (judge verdict: Wrong Answer)

mod = int(1e9+7)
n, m = [int(num) for num in input().split()]

x = [int(x) for x in input().split()]
y = [int(y) for y in input().split()]

sx = [0] * n
sx[0] = x[0]
for i in range(n-1):
    sx[i+1] = sx[i] + x[i+1]
sx.reverse()
sxd = 0  
for i in range(n-1):
    sxd += sx[-i - 2] - x[i] * (n - 1 - i)

sy = [0] * m
sy[0] = y[0]
for k in range(m-1):
    sy[k+1] = sy[k] + y[k+1]
sy.reverse()
syd = 0
for k in range(m-1):
    syd += sy[-k - 2] - y[k] * (m - 1 - k) 

ans = ((sxd % mod) * (syd % mod)) % mod

print(ans)