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)

typedef long long ll;
#include <bits/stdc++.h>
using namespace std;
int main() {
    ll n,m;
    const ll MOD = 1e9+7;
    std::cin >> n>>m;
    vector<ll> x(n);
    vector<ll> y(m);
    for (int i = 0; i < n; i++) {
        std::cin >> x[i];
    }
    for (int i = 0; i < m; i++) {
        std::cin >> y[i];
    }
    ll sum1 = 0;
    ll sum2 = 0;
    // どれくらい重複
    for (int i = 0; i < n-1; i++) {
        sum1 += (x[i+1]-x[i])%MOD*(i+1)%MOD*(n-1-i)%MOD;
        sum1 %= MOD;
    }
    for (int i = 0; i < m-1; i++) {
        sum2 += (y[i+1]-y[i])%MOD*(i+1)%MOD*(m-1-i)%MOD;
        sum2 %= MOD;
    }
    std::cout << sum1%MOD*sum2%MOD << std::endl;
}