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 PyPy3 (7.3.0) (judge verdict: Accepted)

import sys
input = sys.stdin.readline


def main():
    n, m = map(int, input().split())
    x = list(map(int, input().split()))
    y = list(map(int, input().split()))
    
    X = [x[i+1]-x[i] for i in range(n-1)]
    Y = [y[i+1]-y[i] for i in range(m-1)]
    
    mod = pow(10, 9)+7
    for i in range(n-1):
        X[i] = X[i]*(n-i-1)*(i+1)%mod
    
    sum_x = sum(X)%mod
    
    ans = 0
    for j in range(m-1):
        ans += sum_x*Y[j]*(m-j-1)*(j+1)%mod
        ans %= mod
    
    print(ans)
    
    
    
if __name__ == "__main__":
    main()