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: Accepted)

#!/usr/bin/env python3
#
# まず1次元で考える
#   |  |   |  |
#   a  b   c  d
# とあるとき、長さの合計は
#  (b-a) + (c-a) + (d-a) + (c-b) + (d-b) + (d-c)
# = 3d + c - b - 3a
# これは、各点の座標を、<自分より左にある点の数> - <自分より右にある点の数> でかけたものの和である
#
# もとめる面積は X座標、Y座標それぞれについて蒸気を計算した積

MOD = 1000000007

def len_sum(Xs):
    size = len(Xs)
    ret = 0
    n = len(Xs) - 1
    # 負の値にMODをとることを防ぐため、座標の大きい点から計算する
    for x in reversed(Xs):
        ret += n * x
        ret %= MOD
        n -= 2
    return ret

def solve(Xs, Ys):
    x_len_sum = len_sum(Xs)
    y_len_sum = len_sum(Ys)
    return (x_len_sum * y_len_sum) % MOD

N, M = map(int, input().split())
Xs = list(map(int, input().split()))
Ys = list(map(int, input().split()))
print(solve(Xs, Ys))