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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <iomanip>
#include <vector>
#include <cmath>
#include <algorithm>
#include <iomanip>
#include <cstring>
#define rep(i, N) for (int i = 0; i < (int)N; i++)
using namespace std;
typedef long long ll;
const ll LLINF = 9223372036854775807;
const ll MOD = 1000000007;

int main() {
  int n, m; cin >> n >> m;
  ll x[n]; rep(i,n) cin >> x[i];
  ll y[m]; rep(i,m) cin >> y[i];

  ll result = 0, x_sum = 0, y_sum = 0;
  rep(i,n) { x_sum += (2*i-(n-1)) * x[i]; x_sum %= MOD; }
  rep(i,m) { y_sum += (2*i-(m-1)) * y[i]; y_sum %= MOD; }
  result = x_sum * y_sum; result %= MOD;
  cout << result << endl;
  return 0;
}