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 <cstdio>
const int MAXN = 1e5 + 5, mod = 1e9 + 7;
inline int addmod(int a, int b) { return ((a + b) % mod + mod) % mod; }
inline int mulmod(long long a, int b) { return ((a * b) % mod + mod) % mod; }

int n, m, x[MAXN], y[MAXN], suffix[MAXN];
int main() {
	scanf("%d%d", &n, &m);
	for(int i = 1; i <= n; i++) scanf("%d", &x[i]);
	for(int i = 1; i <= m; i++) scanf("%d", &y[i]);

	int sum = 0;
	for(int i = n; i >= 1; i--) suffix[i] = addmod(suffix[i + 1], x[i]);
	for(int i = n; i >= 1; i--) sum = addmod(sum, suffix[i]);
	for(int i = 1; i <= n; i++) sum = addmod(sum, mod - mulmod(n - i + 1, x[i]));

	int sumy = 0;
	suffix[m + 1] = 0;
	for(int i = m; i >= 1; i--) suffix[i] = addmod(suffix[i + 1], y[i]);
	for(int i = m; i >= 1; i--) sumy = addmod(sumy, suffix[i]);
	for(int i = 1; i <= m; i++) sumy = addmod(sumy, mod - mulmod(m - i + 1, y[i]));

	printf("%d\n", mulmod(sum, sumy));
	return 0;
}