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 <bits/stdc++.h>

using namespace std;
typedef long long nagai;

nagai MOD = 1000000007LL;

int main()
{
	int n, m;
	scanf("%d %d", &n, &m);
	vector<int> x(n);
	vector<int> y(m);
	for (auto& a : x)
		scanf("%d", &a);
	for (auto& a : y)
		scanf("%d", &a);
	nagai ans = 0;
	nagai sum = 0;
	for (int j = 0; j < m - 1; ++j)
		sum += 1LL * (j + 1) % MOD * (m - (j + 1)) % MOD * (y[j + 1] - y[j]) % MOD;
	sum %= MOD;
	for (int i = 0; i < n - 1; ++i)
	{
		ans += 1LL * (i + 1) * (n - (i + 1)) % MOD * (x[i + 1] - x[i]) % MOD * sum;
		ans %= MOD;
	}
	cout << ans % MOD << endl;

}