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<iostream>
#include<vector>
using namespace std;
typedef long long ll;

const ll MOD = 1e+9 + 7;
const int MAX_N = 1e+5 + 1;
const int MAX_M = 1e+5 + 1;

ll x[MAX_N], y[MAX_M];

int main() {
    int N, M;
    cin >> N >> M;
    for (int i = 0; i < N; i++) cin >> x[i];
    for (int i = 0; i < M; i++) cin >> y[i];
    vector<ll> sub_x, sub_y;
    for (int i = 0; i < N - 1; i++) {
        sub_x.push_back((i + 1) * (x[i + 1] - x[i]));
    }
    for (int i = 0; i < M - 1; i++) {
        sub_y.push_back((i + 1) * (y[i + 1] - y[i]));
    }
    for (int i = 1; i < sub_x.size(); i++) {
        sub_x[i] = (sub_x[i] + sub_x[i - 1]) % MOD;
    }
    for (int i = 1; i < sub_y.size(); i++) {
        sub_y[i] = (sub_y[i] + sub_y[i - 1]) % MOD;
    }
    ll sum_x = 0, sum_y = 0;
    for (int i = 0; i < sub_x.size(); i++) {
        sum_x = (sum_x + sub_x[i]) % MOD;
    }
    for (int i = 0; i < sub_y.size(); i++) {
        sum_y = (sum_y + sub_y[i]) % MOD;
    }
    cout << (sum_x * sum_y) % MOD << endl;
    return 0;
}