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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php
/*
    Problem URL : http://arc071.contest.atcoder.jp/tasks/arc071_b

    Score  :
    Result :
    Time   : ms
    Memory : KB
 */

ini_set('error_reporting', E_ALL & ~E_NOTICE);

fscanf(STDIN, "%d %d", $n, $m);

define('MOD', pow(10, 9) + 7);

$ans = 0;

$xx = explode(" ", trim(fgets(STDIN)));
$yy = explode(" ", trim(fgets(STDIN)));

$bx = array();
$by = array();
for ($i = 0; $i < $n - 1; $i++) {
    $bx[$i] = ($i + 1) * ($n - $i - 1);
}
for ($i = 0; $i < $m - 1; $i++) {
    $by[$i] = ($i + 1) * ($m - $i - 1);
}
for ($x = 0; $x < $n - 1; $x++) {
    $dx = $xx[$x+1] - $xx[$x];
    $total_x += $bx[$x] * $dx;
    $total_x %= MOD;
}
for ($y = 0; $y < $m - 1; $y++) {
    $dy = $yy[$y+1] - $yy[$y];
    $total_y += $by[$y] * $dy;
    $total_y %= MOD;
}

$ans = $total_x * $total_y % MOD;

echo $ans . PHP_EOL;