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 PHP (5.6.30) (judge verdict: Wrong Answer)

<?php
error_reporting(0);
$stdin = file_get_contents('php://stdin');
$line = explode("\n",$stdin);
$fi = 0;
$cnt = 0;
$list = array();
$key = new stdclass();
foreach($line as $l) {
  if (strlen($l)==0) continue;
  if ($fi == 0) {
    $a = explode(" ",$l);
    $key->A = $a;
    $fi++;
    continue;
  }
  if ($fi > 0) {
    $a = explode(" ",$l);
    $key->X[] = $a;
  }
}
$N = $key->A[0];
$M = $key->A[1];
$X = $key->X[0];
$Y = $key->X[1];
//X,Yの組み合わせから四角形を全部列挙する必要がある。
for($i=0;$i<count($X);$i++) {
  for($j=0;$j<count($Y);$j++) {
    $ary[]=$X[$i].",".$Y[$j];
  }
}
//四角形にする必要があるxが大きく、Yも大きいペアを列挙
$tot=0;
foreach($ary as $p1) {
  foreach($ary as $p2) {
    $p1a = split(",",$p1);
    $p2a = split(",",$p2);
    if ($p1a[0]<$p2a[0] && $p1a[1] < $p2a[1]) {
      //四角形のはず。面積をとる
      $x = $p2a[0] - $p1a[0];
      $y = $p2a[1] - $p1a[1];
      //$sk[]=($x * $y)%1000000009;
      //printf("%s %s\n%d %d %d\n",$p1,$p2,$x,$y,$x*$y) ;
      $tot+=($x*$y)%1000000007;
    }
  }
}
printf("%ld\n",$tot);