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: Accepted)

#include <stdio.h>
#include <inttypes.h>

#define MOD_BY INT32_C(1000000007)

int32_t add(int32_t a, int32_t b) {
	return a + b - MOD_BY * (a + b >= MOD_BY);
}

int32_t sub(int32_t a, int32_t b) {
	return b == 0 ? a : add(a, MOD_BY - b);
}

int32_t mul(int32_t a, int32_t b) {
	int32_t r = 0;
	while (b > 0) {
		if (b & 1) r = add(r, a);
		a = add(a, a);
		b >>= 1;
	}
	return r;
}

int32_t n, m;
int32_t x[114514];
int32_t y[114514];

int32_t x_ruiseki[114514], y_ruiseki[114514];

int main(void) {
	int32_t i, k;
	int32_t xsum = 0, ysum = 0;
	if (scanf("%" SCNd32 "%" SCNd32, &n, &m) != 2) return 1;
	for (i = 1; i <= n; i++) {
		if (scanf("%" SCNd32, &x[i]) != 1) return 1;
		if (x[i] < 0) x[i] += MOD_BY;
		x_ruiseki[i] = add(x_ruiseki[i - 1], x[i]);
	}
	for (i = 1; i <= m; i++) {
		if (scanf("%" SCNd32, &y[i]) != 1) return 1;
		if (y[i] < 0) y[i] += MOD_BY;
		y_ruiseki[i] = add(y_ruiseki[i - 1], y[i]);
	}
	for (i = 1; i < n; i++) {
		xsum = sub(xsum, mul(sub(n, i), x[i]));
		xsum = add(xsum, sub(x_ruiseki[n], x_ruiseki[i]));
	}
	for (k = 1; k < m; k++) {
		ysum = sub(ysum, mul(sub(m, k), y[k]));
		ysum = add(ysum, sub(y_ruiseki[m], y_ruiseki[k]));
	}
	printf("%" PRId32 "\n", mul(xsum, ysum));
	return 0;
}

/*

\begin{eqnarray*}
&& \sum_{i=1}^{n-1} \sum_{j=i+1}^{n} \sum_{k=1}^{m-1} \sum_{l=k+1}^{m} (x_j - x_i) (y_l - y_k) \\
&=& \sum_{i=1}^{n-1} \sum_{j=i+1}^{n} (x_j - x_i) \sum_{k=1}^{m-1} \sum_{l=k+1}^{m} (y_l - y_k) \\
&=& \sum_{i=1}^{n-1} \left\{ -(n-i) x_i + \sum_{j=i+1}^{n} x_j \right\}
    \sum_{k=1}^{m-1} \left\{ -(m-k) y_k + \sum_{l=k+1}^{m} y_l \right\}
\end{eqnarray*}

*/