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 "debug.h"
#include <string.h>
#include <limits.h>
#include <map>
#include <set>
#include <vector>
#include <algorithm>
using namespace std;

#define M 1000000007
#define MAXN 100000

int m, n;
long a[MAXN], b[MAXN]; 

int input() {
	if (scanf("%d %d", &m, &n) < 0) return 0;
	for (int i=0; i<m; i++) scanf("%ld", &a[i]);
	for (int i=0; i<n; i++) scanf("%ld", &b[i]);
	return 1;
}

void init() {
}

long calc(long *a, int n) {
	n--;
	for (int i=0; i<n; i++)
		a[i] = a[i+1]-a[i];
	long s = 0, r = 0;
	for (int i=0; i<n; i++) {
		s += a[i] * (i+1);
		r += s;
		s %= M;
		r %= M;
	}
	return r;
}

long solve() {
	return calc(a, m) * calc(b, n) % M;
}

void output(long ans) {
	printf("%ld\n", ans);
}

void cleanup() {
}

int main() {
	while (input()) {
		init();
		output(solve());
		cleanup();
		//break;
	}
}