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: Runtime Error)

#include <bits/stdc++.h>

using namespace std;

typedef long long int lli;

int main() {
    const lli mod = 1000000007;
    int n, m;

    cin >> n >> m;
    vector<lli> x(n), y(m), sx(n+1, 0), sy(n+1, 0);
    for (int i=0; i<n; i++) {
        cin >> x[i];
        x[i] += (lli)1e+9;
        sx[i+1] = (x[i]+sx[i]) % mod;
    }
    for (int i=0; i<m; i++) {
        cin >> y[i];
        y[i] += (lli)1e+9;
        sy[i+1] = (y[i]+sy[i]) % mod;
    }

    lli X = 0;
    for (int i=1; i<n; i++) {
        X += mod + (x[i]*i)%mod - (mod+sx[i]-sx[0])%mod;    // mod + (mod + sx[n] - sx[i])%mod - (x[i-1] * (lli)(n-i))%mod;
        X %= mod;
    }
    lli Y = 0;
    for (int i=1; i<m; i++) {
        Y += mod + (y[i]*i)%mod - (mod+sy[i]-sy[0])%mod;    // mod + (mod + sy[m] - sy[i])%mod - (y[i-1] * (lli)(m-i))%mod;
        Y %= mod;
    }

    cout << (X * Y) % mod << endl;

    cout << "Hello" << endl;

    return 0;
}