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: Time Limit Exceeded)

MOD = 10 ** 9 + 7
n, m = map(int, input().split())
x = list(map(int, input().split()))
y = list(map(int, input().split()))

# 前計算
for i in range(n - 1):
    x[i] = x[i + 1] - x[i]

for i in range(m - 1):
    y[i] = y[i + 1] - y[i]

N = [n - 1]
for i in range((n)//2 - 1):
    N.append((N[i] + (n - 1 - 2 * (i + 1))) % MOD)

M = [m - 1]
for i in range((m)//2 - 1):
    M.append((M[i] + (m - 1- 2 * (i + 1))) % MOD)

if N[0] % 2 == 0:
    N += N[::-1]
elif N[0] != 1:
    N += N[1::-1]
if M[0] % 2 == 0:
    M += M[::-1]
elif M[0] != 1:
    M += M[1::-1]

# print (x)
# print (y)
# print (N)
# print (M)

if len(x) - 1 != len(N):
    while True:
        pass

if len(y) - 1 != len(M):
    while True:
        pass


X_sum = 0
for i in range(n - 1):
    X_sum += x[i] * N[i]
    X_sum %= MOD

Y_sum = 0
for i in range(m - 1):
    Y_sum += y[i] * M[i]
    Y_sum %= MOD

print ((X_sum * Y_sum) % MOD)