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<stdlib.h>
#include<string.h>
#define ll long long
#define MOD 1000000007LL
#define len 12
int scan(int*a,int n){int*p;char*ptr_c,*buf;buf=malloc(n*len);p=a;ptr_c=buf;fgets(buf,n*len,stdin);while(n--){*p++=atoi(ptr_c);ptr_c=strchr(ptr_c+1,32)+1;}}

int main(){
	ll a,b;
	int *x,*y,*ptr,n,m,i;

	scanf("%d%d\n",&n,&m);
	x=(int*)malloc(n*sizeof(int));
	y=(int*)malloc(m*sizeof(int));
	scan(x,n);
	scan(y,m); 

	for(i=1,a^=a,ptr=x,++n;i<n;++i)
		a+=*ptr++*((ll)i+i-n)%MOD;
		
	for(i=1,b^=b,ptr=y,++m;i<m;++i)
		b+=*ptr++*((ll)i+i-m)%MOD;
	
	printf("%lld\n",(a%MOD)*(b%MOD)%MOD);
	
	free(x);
	free(y);
	return 0;
}