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>

#define MOD 1000000007

#define N_MAX 100000
#define M_MAX N_MAX

typedef long long ll;

int n, m;
ll x[N_MAX], y[M_MAX];
ll cx[N_MAX], cy[M_MAX];


int main(void)
{
	int i;
	ll w, h;

	while(scanf("%d%d", &n, &m)==2)
	{
		for(i=0;i<n;i++) scanf("%lld", &x[i]);
		for(i=0;i<m;i++) scanf("%lld", &y[i]);

		for(i=0;i+1<n;i++)
		{
			if(i==0) cx[i]=n;
			else cx[i]=cx[i-1]+n-i*2;
		}

		w=0;
		cx[0]=0;
		for(i=1;i<n;i++)
		{
			cx[i]=(cx[i-1]+n+1-i*2)%MOD;
			w=(w+(x[i]-x[i-1])*cx[i])%MOD;
		}
		h=0;
		cy[0]=0;
		for(i=1;i<m;i++)
		{
			cy[i]=(cy[i-1]+m+1-i*2)%MOD;
			h=(h+(y[i]-y[i-1])*cy[i])%MOD;
		}
		printf("%lld\n", (w*h)%MOD);
	}

	return 0;
}