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<cstdio>
#include<cstring>
#include<algorithm>
#define N 100005
using namespace std;
const int mod = 1e9+7;
inline int read(){
	int sum = 0, t = 1; char ch = getchar();
	while(ch < '0' || ch > '9'){ if(ch == '-') t = -1; ch = getchar(); }
	while(ch >= '0' && ch <= '9'){ sum = sum * 10 + ch - '0'; ch = getchar(); }
	return sum * t;
}

int n, m, S, S_;
int x[N], y[N];

void upd(int &x, int y){ x += y; if(x >= mod) x -= mod; }

int main(){
	n = read(); m = read();
	for(int i = 1; i <= n; i++) x[i] = read(), upd(x[i], mod), upd(S, 1LL * x[i] * (n - i * 2 + 1 + mod) % mod);
	for(int i = 1; i <= m; i++) y[i] = read(), upd(y[i], mod), upd(S_, 1LL * y[i] * (m - i * 2 + 1 + mod) % mod);
	printf("%lld\n", 1LL * S * S_ % mod);
}