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 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <stdio.h>
#define MOD 1000000007

int n, m;
int x[100000], y[100000];
long long int scale_x[100000], scale_y[100000];

int main(void) {
	int i, j;
	long long int ans = 0;
	long long int area;

	scanf("%d%d", &n, &m);
	for (i = 0; i < n; i++) {
		scanf("%d", &x[i]);
	}
	for (i = 0; i < m; i++) {
		scanf("%d", &y[i]);
	}
	for (i = 1; i < n; i++) 
		scale_x[i] = i * (n - i);
	for (i = 1; i < m; i++) 
		scale_y[i] = i * (m - i);

	for (i = 1; i < n; i++) {
		for (j = 1; j < m; j++) {
			area = ((long long int)(x[i] - x[i - 1]) * (y[j] - y[j - 1])) % MOD;
			ans += area * scale_x[i] % MOD * scale_y[j] % MOD;
			ans %= MOD;
		}
	}
	printf("%lld\n", ans);

	return 0;
}